ĐỀ KHẢO SÁT ĐẦU NĂM LỚP 9 MÔN TOÁN

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    !"# $ %&'()(*+,-./-(#01&234 567$888 9:;$ <:3&=>>&:+)>?*&*(1&@+3&=>A B-A/C+)$ DEF%;GF48 E8%;GF48 E8F%FG;48 E8F%;GF4 9:8$H1+)&(I.>?*1&JK+)3LM+&NFGONPQ,-$ DEA EA EA EA 9:R$&S1&JK+)3LM+&A T1&JK+)3LM+&>U+)&(I.FP83&M.>U )(V3LW,-$ DE.P; E.P; E.P8 E.P8 9:O$(X(1&JK+)3LM+&F8GQP03*YJZ> DEFPQ EFPA EFPA EFPAB-F PA 9:Q$(V3LW>?*/(T:3&=>F8[8F\[\83](FP^^B-\P8R,-$ DE^^00 E;0000 E^^00 E^Q00 9:_$23)`+/(T:3&=>8 A Ba(*b03*YJZ> DER* E^* ER* E^* 9:^$(c:d(I+FV>YW+&>?*1&JK+) 3LM+&$A ,-$ DEA EA EA EA 9:e$&@+3f>&Y*3&=>A3&-+&+&@+3gh3* YJZ>$ DEA EF A EF%F[R4%FR4 EF%F#4%F[#4 9:#$&S3*.)(V>D>U ,-3L:+)Y(T.>?*Di,-3L:+)Y(T.>?*Di/(j3 P80>.E&(YU Ykl-(>]+&/C+)$ DE;0>. E80>. ER0>. EO0>. 9:;0$m\>&`+>@:Y2+)Ej: DYn+)l]+)Ba( Dooo3&pS3q6r*3&M DoooYn+)l]+)   Ba( D3&pS3q6r$ DE* EA E; E8 9:;;$@:+-S6*:Y@\6*(s DEM+&3&S(>U.k3)U>B:t+),-&M+&B:t+) EM+&3&*+)>U&*(YJ'+)>&uS/C+)+&*:,-&M+&3&*+)>@+ Ev+)>V>)U>3LS+)3=)(V>/C+)R_00E EM+&>&w+&H3>U&*(YJ'+)>&uS/C+)+&*:,-&M+&B:t+)E 9:;8$ k3&M+&&k1>&w+&H3>U DE_.x3h_Yq+&h;8>]+& Ee.x3h_Yq+&h;8>]+& E_.x3h;8Yq+&he>]+& E_.x3heYq+&h;8>]+& 9:;R$&S y +>@:3L* z ,K { (Y: | +)E &JK+)3L} { +&A>S | 3@ y 1+)&(~ y .,* { $ DEA EA EA EA 9:;O$*.)(V>>U>]+&YV\/C+)*h>&(c:>*S3JK+)=+)/C+)&3&Ml(I+3f>&,-$ DE*& E8*& EA *& EA *& 9:;Q$a()(V3LW+-S>?*F3&M>•+3&=>A>U +)&€* + − 2 x 2 x x + − + 2 x 1 2x 4x 2 { } #i ;− { } #i;− { } ;i ;− { } #i #− 8 R ; ; x m x x x − − + = − + QQ− QQ− aa Q 8 − 8 R ; 0 ; ; x x x x + + = + + − ;x ≠ ;h 8x x≠ ≠ 8x ≠ Rx ≠ R #x x− 8 % #4x x − 8 % #4x + ; a ( ) ( ) ( ) ( ) F F 8F 8 F R 8 F ; F ; F R + = − + + − { } 6 0i e= − { } 6 0= ; 6 0i ^   = −     { } 6 0iR= 8 R ; 8 8O −x DEFAA EFPA EFAA EFAA 9:;_$&S y +>@:3L* z ,K { (Y: | +)E L: y >Yt | (FJ | +)>: z *&} { +&3&*+)>@+,* { $ DEJK { +)>&p | S>: z *&} { +&3&*+)>@+E EJK { +)3&• z +)Y(•:*3L:+)Y(~ z .>* | >>* y +&/~+>: z *&} { +&3&*+)>@+E EJK { +)3&• z +)B:t+))S | >BK | (&*(Y* | \>: z *&} { +&3&*+)>@+E EJK { +)3&• z +)Y(•:*3L:+)Y(~ z .&*(Y* | \>: z *&} { +&3&*+)>@+E 9:;^$)&(I.>?*/‚31&JK+)3LM+&A,-$ DEA EA EA EA 9:;e$ k3&M+&>&w+&H3>U>&:B(,-_0>.h>&(c: Lk+)/C+) AE(I+3f>&>?*&M+&>&w+&H3,-$ DE^8 A E8;_ A E#0 A EOe A 9:;#$LS+)3*.)(V>B:t+)>U)U>+&`+ A3&M3q 6r)(w*>]+&Yr(B->]+&dcYJZ>)`(,-$ DE6(+ A E>S6 A E>S3 A E3*+ A 9:80$a()(V3LW+-S>?*F3&MRFGQd&t+)+&ƒ&K+8F DE&t+)>U)(V3LW+-SEFA Q EFAQ E `(F 9:8;$f+&)(V3LW/(T:3&=>A3*YJZ> DE80 E;e E88 ER0 9:88$&S&M+&3&S(Dh,-)(*SY(T.>?*&*(YJ'+)>&uSE(j3DPQ>.hDPR>.E&(YUl(I+ 3f>&&M+&3&S(D/C+)$ DE;8>.8 E8O>.8 EOe>.8 E#_>.8 9:8R$&S y +>@:3L* z ,K { (Y: | +)E )&(~ y .>: z *1&JK+)3L} { +&%RFG;4%FGR4%8F[Q4P0,* { $ DEAB* { A EAB* { A EAB* { A EAB* { A 9:8O$&JK+)3LM+&A >U+)&(I.$ DEFP; EFP; EFP8 EFP8 9:8Q$j3•:X>?*1&u13f+&A,-$ DEA EA EA EA 9:8_$&S y +d~ | 3•:* z Y: | +)E%F[8\4RP DEFR[RF8\[_F\8[e\R EFR[_F8\[;8F\8[e\R EFR[_F8\[_F\8[e\R EFR[_F8\[;8F\8[8\R 9:8^$j3•:X1&@+3f>&Y*3&=>F88F[;3&-+&+&@+3g,-$ DE%F[;48 E%FG;48 EG%FG;48 EG%F[;48 9:8e$&S y +>@:3L* z ,K { (Y: | +)EA DEA EA EA EA 9:8#$M+&/M+&&-+&>U.k3>]+&/C+)*h>&(c:>*S3JK+)=+)/C+)&3&Ml(I+3f>&,-$ DE*& E8*& ER*& EO*& 9:R0$ k3&M+&&k1>&w+&H3>U>&:B(YV\,-R0>.h>&(c:>*S>?*&M+&&k1,-Q>.E(I+3f>&F:+)•:*+& >?*&M+&&k1,-$ DE;Q0 A ER00 A E;00 A E^Q A 9:R;$&S AB:t+)3](hYJ'+)>*SE(j3 DPe>.hP_>.Ekl-(YJ'+)>*S,-$ DEOhe>. E;0>. E;8>. E;Q>. 9:R8$&S&M+&3&*+)D%D„„4>U >V>YJ'+)>&uS>…3+&*:3](E(j3AiDP 〉 8 ; 8 ; 〈 8 ; ≥ 8 ; _  _ R x x x+ > Ox > Ox < Qx > Qx < 8 R 8 cm 8 cm 8 cm 8 cm α αααα ≥≤ O#$;#_8QE;_ + ; F R = Q F 8 − = F R= Q F 8 − = ; F h F R R − = = − Q F 8 = ; F h F R R = = Q F 8 − = 8 Rx + = R E Q R 8 − − x x x x 8 Q ; xxQ ; 8 ; Qx − ; Qx − 8 8 F RF\ P 8;\ ^F\ ^ x y − ^ x y^ x y y x − − R ^ x y y − 8 cm 8 cm 8 cm 8 cm ABC ∆ ; R OA OC= 8>.Ekl-(>]+&/C+)$ DER>. E_>. E#>. E;8>. 9:RR$&S1&JK+)3LM+&A a(.P;3&M1&JK+)3LM+&3L~+>U+)&(I. ,-$ DEFP; EFPO EFP;iFPO EFP;iFPO 9:RO$(T:3&=>DPNFGRN[FG8%Ba(FGRb046*:d&(L23)`+,-$ DEDP8FGQ EDP8F[Q EDP; EDPQ 9:RQ$H1&Z1>V>)(V3LW>?*FYTRF8P8F,- DE†0‡ EA E†A‡ E†0iA‡ 9:R_$LS+)3*.)(V>B:t+)>U)U>+&`+ A3&M3q 6r)(w*>]+&Yr(B->]+&&:\c+YJZ>)`(,-$ DE6(+ A E>S6 A E>S3 A E3*+ A 9:R^$&SAB:t+)3](Dh>UDP#>.h DP;8>.h6(++&H+)(V3LW+-S6*:Y@\$ DE0he E0h_ E;h0 E0h^Q 9:Re$&S3*.)(V>DhDP;0>.hP#>.E!‚\Y(T.3L~+>]+&6*S>&SPR>.E!‚\ Y(T.h3L~+>]+&D6*S>&SDPPO>.E`(ˆ,-)(*SY(T.>?*B-D *>U„„BM3LS+)3*.)(V>>U$ DEA EA EA EA 9:R#$&S&M+&B:t+)>UYkl-(>?*>]+&,-;>.Ekl-(YJ'+)>&uS&M+&B:t+),- DE;hQ>. E8>. EA>. EA>. 9:O0$&S3*.)(V>Dh „„% A Dh  A D4Y‰+)3&=>Y2+),- DEA EA EA EA Š3 8 R ; ; x m x x x − − + = − + 8 R R 8 R 8 α αααα ABC ∆ CD CH CB CG = CD CH CB HG = BD GH BC HC = BD CH BC CG = 8h;8 ∈∈ AN AM BC MN = AB AM BC MN = AN AM MN BC = AB AM BC AN =     !"# $ %&'()(*+,-./-(#01&234 567$OOO 9:;$&S y +>@:3L* z ,K { (Y: | +)E )&(~ y .>: z *1&JK+)3L} { +&%RFG;4%FGR4%8F[Q4P0,* { $ DEAB* { A EAB* { A EAB* { A EAB* { A 9:8$&@+3f>&Y*3&=>A3&-+&+&@+3gh3* YJZ>$ DEA EF A EF%F[R4%FR4 EF%F#4%F[#4 9:R$&S3*.)(V>Dh „„% A Dh  A D4Y‰+)3&=>Y2+),- DEA EA EA EA 9:O$LS+)3*.)(V>B:t+)>U)U>+&`+ A3&M3q 6r)(w*>]+&Yr(B->]+&dcYJZ>)`(,-$ DE6(+ A E>S6 A E>S3 A E3*+ A 9:Q$a()(V3LW+-S>?*F3&MRFGQd&t+)+&ƒ&K+8F DE&t+)>U)(V3LW+-SEFA Q EFAQ E `(F 9:_$ <:3&=>>&:+)>?*&*(1&@+3&=>A B-A/C+)$ DEF%;GF48 E8%;GF48 E8F%FG;48 E8F%;GF4 9:^$(c:d(I+FV>YW+&>?*1&JK+) 3LM+&$A ,-$ DEA EA EA EA 9:e$)&(I.>?*/‚31&JK+)3LM+&A,-$ DEA EA EA EA 9:#$&S y +>@:3L* z ,K { (Y: | +)EA DEA EA EA EA 9:;0$ k3&M+&&k1>&w+&H3>U>&:B(YV\,-R0>.h>&(c:>*S>?*&M+&&k1,-Q>.E(I+3f>&F:+) •:*+&>?*&M+&&k1,-$ DE;Q0 A ER00 A E;00 A E^Q A 9:;;$&S y +>@:3L* z ,K { (Y: | +)E &JK+)3L} { +&A>S | 3@ y 1+)&(~ y .,* { $ DEA EA EA EA 9:;8$m\>&`+>@:Y2+)Ej: DYn+)l]+)Ba( Dooo3&pS3q6r*3&M DoooYn+)l]+)   Ba( D3&pS3q6r$ DE* EA E; E8 9:;R$(V3LW>?*/(T:3&=>F8[8F\[\83](FP ^^B-\P8R,-$ DE^^00 E;0000 E^^00 E^Q00 9:;O$@:+-S6*:Y@\6*(s ; F R = Q F 8 − = F R= Q F 8 − = ; F h F R R − = = − Q F 8 = ; F h F R R = = Q F 8 − = R #x x− 8 % #4x x − 8 % #4x + ∈∈ AN AM BC MN = AB AM BC MN = AN AM MN BC = AB AM BC AN = α αααα ≥≤ + − 2 x 2 x x + − + 2 x 1 2x 4x 2 8 R ; 0 ; ; x x x x + + = + + − ;x ≠ ;h 8x x≠ ≠ 8x ≠ Rx ≠ _  _ R x x x+ > Ox > Ox < Qx > Qx < 8 8 F RF\ P 8;\ ^F\ ^ x y − ^ x y^ x y y x − − R ^ x y y − 8 cm 8 cm 8 cm 8 cm ( ) ( ) ( ) ( ) F F 8F 8 F R 8 F ; F ; F R + = − + + − { } 6 0i e= − { } 6 0= ; 6 0i ^   = −     { } 6 0iR= ; a DEM+&3&S(>U.k3)U>B:t+),-&M+&B:t+) EM+&3&*+)>U&*(YJ'+)>&uS/C+)+&*:,-&M+&3&*+)>@+ Ev+)>V>)U>3LS+)3=)(V>/C+)R_00E EM+&>&w+&H3>U&*(YJ'+)>&uS/C+)+&*:,-&M+&B:t+)E 9:;Q$&S&M+&3&*+)D%D„„4>U >V>YJ'+)>&uS>…3+&*:3](E(j3AiDP 8>.Ekl-(>]+&/C+)$ DER>. E_>. E#>. E;8>. 9:;_$H1+)&(I.>?*1&JK+)3LM+&NFGONPQ,-$ DEA EA EA EA 9:;^$*.)(V>>U>]+&YV\/C+)*h>&(c:>*S 3JK+)=+)/C+)&3&Ml(I+3f>&,-$ DE*& E8*& EA *& EA *& 9:;e$(T:3&=>DPNFGRN[FG8%Ba(FGRb04 6*:d&(L23)`+,-$ DEDP8FGQ EDP8F[Q EDP; EDPQ 9:;#$&S1&JK+)3LM+&A T1&JK+)3LM+&>U+)&(I.FP83&M.>U )(V3LW,-$ DE.P; E.P; E.P8 E.P8 9:80$&S y +d~ | 3•:* z Y: | +)E%F[8\4RP DEFR[RF8\[_F\8[e\R EFR[_F8\[;8F\8[e\R EFR[_F8\[_F\8[e\R EFR[_F8\[;8F\8[8\R 9:8;$&JK+)3LM+&A >U+)&(I.$ DEFP; EFP; EFP8 EFP8 9:88$&S AB:t+)3](hYJ'+)>*SE(j3 DPe>.hP_>.Ekl-(YJ'+)>*S,-$ DEOhe>. E;0>. E;8>. E;Q>. 9:8R$(X(1&JK+)3LM+&F8GQP03*YJZ> DEFPQ EFPA EFPA EFPAB-F PA 9:8O$ k3&M+&>&w+&H3>U>&:B(,-_0>.h>&(c: Lk+)/C+) AE(I+3f>&>?*&M+&>&w+&H3,-$ DE^8 A E8;_ A E#0 A EOe A 9:8Q$LS+)3*.)(V>B:t+)>U)U>+&`+ A3&M3q 6r)(w*>]+&Yr(B->]+&&:\c+YJZ>)`(,-$ DE6(+ A E>S6 A E>S3 A E3*+ A 9:8_$f+&)(V3LW/(T:3&=>A3*YJZ> DE80 E;e E88 ER0 9:8^$&S y +>@:3L* z ,K { (Y: | +)E L: y >Yt | (FJ | +)>: z *&} { +&3&*+)>@+,* { $ DEJK { +)>&p | S>: z *&} { +&3&*+)>@+E EJK { +)3&• z +)Y(•:*3L:+)Y(~ z .>* | >>* y +&/~+>: z *&} { +&3&*+)>@+E EJK { +)3&• z +)B:t+))S | >BK | (&*(Y* | \>: z *&} { +&3&*+)>@+E EJK { +)3&• z +)Y(•:*3L:+)Y(~ z .&*(Y* | \>: z *&} { +&3&*+)>@+E 9:8e$a()(V3LW+-S>?*F3&M>•+3&=>A>U +)&€* DEFAA EFPA EFAA EFAA 9:8#$&S3*.)(V>D>U ,-3L:+)Y(T.>?* Di,-3L:+)Y(T.>?*Di/(j3 P80>.E&( YUYkl-(>]+&/C+)$ DE;0>. E80>. ER0>. EO0>. 9:R0$&S&M+&3&S(Dh,-)(*SY(T.>?*&*(YJ'+)>&uSE(j3DPQ>.hDPR>.E&(YUl(I+ 3f>&&M+&3&S(D/C+)$ DE;8>.8 E8O>.8 EOe>.8 E#_>.8 9:R;$&S1&JK+)3LM+&A a(.P;3&M1&JK+)3LM+&3L~+>U+)&(I. ,-$ DEFP; EFPO EFP;iFPO EFP;iFPO ; R OA OC= { } #i ;− { } #i;− { } ;i ;− { } #i #− 8 R ; 8 8 R ; ; x m x x x − − + = − + 8 Rx + = ABC ∆ QQ− QQ− 8 R 8 cm 8 cm 8 cm 8 cm α αααα O#$;#_8QE;_ + 8O −x 〉 8 ; 8 ; 〈 8 ; ≥ 8 ; 8 R ; ; x m x x x − − + = − + 9:R8$&SAB:t+)3](Dh>UDP#>.h DP;8>.h6(++&H+)(V3LW+-S6*:Y@\$ DE0he E0h_ E;h0 E0h^Q 9:RR$ k3&M+&&k1>&w+&H3>U DE_.x3h_Yq+&h;8>]+& Ee.x3h_Yq+&h;8>]+& E_.x3h;8Yq+&he>]+& E_.x3heYq+&h;8>]+& 9:RO$M+&/M+&&-+&>U.k3>]+&/C+)*h>&(c:>*S3JK+)=+)/C+)&3&Ml(I+3f>&,-$ DE*& E8*& ER*& EO*& 9:RQ$&S&M+&B:t+)>UYkl-(>?*>]+&,-;>.Ekl-(YJ'+)>&uS&M+&B:t+),- DE;hQ>. E8>. EA>. EA>. 9:R_$23)`+/(T:3&=>8 A Ba(*b03*YJZ> DER* E^* ER* E^* 9:R^$H1&Z1>V>)(V3LW>?*FYTRF8P8F,- DE†0‡ EA E†A‡ E†0iA‡ 9:Re$&S3*.)(V>DhDP;0>.hP#>.E !‚\Y(T.3L~+>]+&6*S>&SPR>.E!‚\ Y(T.h3L~+>]+&D6*S>&SDPPO>.E `(ˆ,-)(*SY(T.>?*B-D *>U„„BM3LS+)3*.)(V>>U$ DEA EA EA EA 9:R#$j3•:X>?*1&u13f+&A,-$ DEA EA EA EA 9:O0$j3•:X1&@+3f>&Y*3&=>F88F[;3&-+&+&@+3g,-$ DE%F[;48 E%FG;48 EG%FG;48 EG%F[;48 Š3 ABC ∆ 8h;8 aa Q 8 − 8 R R 8 R 8 CD CH CB CG = CD CH CB HG = BD GH BC HC = BD CH BC CG = R E Q R 8 − − x x x x 8 Q ; xxQ ; 8 ; Qx − ; Qx −     !"# $ %&'()(*+,-./-(#01&234 567$___ 9:;$&S&M+&B:t+)>UYkl-(>?*>]+&,-;>.Ekl-(YJ'+)>&uS&M+&B:t+),- DE;hQ>. E8>. EA>. EA>. 9:8$&S&M+&3&*+)D%D„„4>U >V>YJ'+)>&uS>…3+&*:3](E(j3AiDP 8>.Ekl-(>]+&/C+)$ DER>. E_>. E#>. E;8>. 9:R$H1&Z1>V>)(V3LW>?*FYTRF8P8F,- DE†0‡ EA E†A‡ E†0iA‡ 9:O$23)`+/(T:3&=>8 A Ba(*b03*YJZ> DER* E^* ER* E^* 9:Q$f+&)(V3LW/(T:3&=>A3*YJZ> DE80 E;e E88 ER0 9:_$j3•:X1&@+3f>&Y*3&=>F88F[;3&-+&+&@+3g,-$ DE%F[;48 E%FG;48 EG%FG;48 EG%F[;48 9:^$&S y +>@:3L* z ,K { (Y: | +)E )&(~ y .>: z *1&JK+)3L} { +&%RFG;4%FGR4%8F[Q4P0,* { $ DEAB* { A EAB* { A EAB* { A EAB* { A 9:e$&S y +>@:3L* z ,K { (Y: | +)EA DEA EA EA EA 9:#$LS+)3*.)(V>B:t+)>U)U>+&`+ A3&M3q 6r)(w*>]+&Yr(B->]+&dcYJZ>)`(,-$ DE6(+ A E>S6 A E>S3 A E3*+ A 9:;0$&S&M+&3&S(Dh,-)(*SY(T.>?*&*(YJ'+)>&uSE(j3DPQ>.hDPR>.E&(YUl(I+ 3f>&&M+&3&S(D/C+)$ DE;8>.8 E8O>.8 EOe>.8 E#_>.8 9:;;$&S3*.)(V>D>U ,-3L:+)Y(T.>?*Di,-3L:+)Y(T.>?*Di/(j3 P80>.E&(YU Ykl-(>]+&/C+)$ DE;0>. E80>. ER0>. EO0>. 9:;8$&S1&JK+)3LM+&A a(.P;3&M1&JK+)3LM+&3L~+>U+)&(I. ,-$ DEFP; EFPO EFP;iFPO EFP;iFPO 9:;R$@:+-S6*:Y@\6*(s DEM+&3&S(>U.k3)U>B:t+),-&M+&B:t+) EM+&3&*+)>U&*(YJ'+)>&uS/C+)+&*:,-&M+&3&*+)>@+ Ev+)>V>)U>3LS+)3=)(V>/C+)R_00E EM+&>&w+&H3>U&*(YJ'+)>&uS/C+)+&*:,-&M+&B:t+)E 9:;O$(c:d(I+FV>YW+&>?*1&JK+) 3LM+&$A ,-$ DEA EA EA 8h;8 ; R OA OC= 8 R R 8 R 8 aa Q 8 − O#$;#_8QE;_ + ; F R = Q F 8 − = F R= Q F 8 − = ; F h F R R − = = − Q F 8 = ; F h F R R = = Q F 8 − = 8 8 F RF\ P 8;\ ^F\ ^ x y − ^ x y^ x y y x − − R ^ x y y − α αααα 8 R ; ; x m x x x − − + = − + 8 R ; 0 ; ; x x x x + + = + + − ;x ≠ ;h 8x x≠ ≠ 8x ≠ Rx ≠ EA 9:;Q$M+&/M+&&-+&>U.k3>]+&/C+)*h>&(c:>*S3JK+)=+)/C+)&3&Ml(I+3f>&,-$ DE*& E8*& ER*& EO*& 9:;_$&S3*.)(V>DhDP;0>.hP#>.E!‚\Y(T.3L~+>]+&6*S>&SPR>.E!‚\ Y(T.h3L~+>]+&D6*S>&SDPPO>.E`(ˆ,-)(*SY(T.>?*B-D *>U„„BM3LS+)3*.)(V>>U$ DEA EA EA EA 9:;^$&JK+)3LM+&A >U+)&(I.$ DEFP; EFP; EFP8 EFP8 9:;e$&S1&JK+)3LM+&A T1&JK+)3LM+&>U+)&(I.FP83&M.>U )(V3LW,-$ DE.P; E.P; E.P8 E.P8 9:;#$(X(1&JK+)3LM+&F8GQP03*YJZ> DEFPQ EFPA EFPA EFPAB-F PA 9:80$LS+)3*.)(V>B:t+)>U)U>+&`+ A3&M3q 6r)(w*>]+&Yr(B->]+&&:\c+YJZ>)`(,-$ DE6(+ A E>S6 A E>S3 A E3*+ A 9:8;$&S AB:t+)3](hYJ'+)>*SE(j3 DPe>.hP_>.Ekl-(YJ'+)>*S,-$ DEOhe>. E;0>. E;8>. E;Q>. 9:88$&S y +>@:3L* z ,K { (Y: | +)E L: y >Yt | (FJ | +)>: z *&} { +&3&*+)>@+,* { $ DEJK { +)>&p | S>: z *&} { +&3&*+)>@+E EJK { +)3&• z +)Y(•:*3L:+)Y(~ z .>* | >>* y +&/~+>: z *&} { +&3&*+)>@+E EJK { +)3&• z +)B:t+))S | >BK | (&*(Y* | \>: z *&} { +&3&*+)>@+E EJK { +)3&• z +)Y(•:*3L:+)Y(~ z .&*(Y* | \>: z *&} { +&3&*+)>@+E 9:8R$&SAB:t+)3](Dh>UDP#>.h DP;8>.h6(++&H+)(V3LW+-S6*:Y@\$ DE0he E0h_ E;h0 E0h^Q 9:8O$a()(V3LW+-S>?*F3&M>•+3&=>A>U +)&€* DEFAA EFPA EFAA EFAA 9:8Q$H1+)&(I.>?*1&JK+)3LM+&NFGONPQ,-$ DEA EA EA EA 9:8_$ <:3&=>>&:+)>?*&*(1&@+3&=>A B-A/C+)$ DEF%;GF48 E8%;GF48 E8F%FG;48 E8F%;GF4 9:8^$ k3&M+&&k1>&w+&H3>U DE_.x3h_Yq+&h;8>]+& Ee.x3h_Yq+&h;8>]+& E_.x3h;8Yq+&he>]+& E_.x3heYq+&h;8>]+& 9:8e$*.)(V>>U>]+&YV\/C+)*h>&(c:>*S3JK+)=+)/C+)&3&Ml(I+3f>&,-$ DE*& E8*& EA *& EA *& 9:8#$j3•:X>?*1&u13f+&A,-$ DEA EA EA EA 9:R0$&S y +d~ | 3•:* z Y: | +)E%F[8\4RP DEFR[RF8\[_F\8[e\R EFR[_F8\[;8F\8[e\R EFR[_F8\[_F\8[e\R EFR[_F8\[;8F\8[8\R 9:R;$ k3&M+&>&w+&H3>U>&:B(,-_0>.h>&(c: Lk+)/C+) AE(I+3f>&>?*&M+&>&w+&H3,-$ DE^8 A E8;_ A E#0 A EOe A CD CH CB CG = CD CH CB HG = BD GH BC HC = BD CH BC CG = 8 Rx + = 8 R ; ; x m x x x − − + = − + QQ− QQ− α αααα ABC ∆ ABC ∆ 8O −x 〉 8 ; 8 ; 〈 8 ; ≥ 8 ; { } #i ;− { } #i;− { } ;i ;− { } #i #− + − 2 x 2 x x + − + 2 x 1 2x 4x 2 8 R ; 8 R E Q R 8 − − x x x x 8 Q ; xxQ ; 8 ; Qx − ; Qx − 8 R 8 cm 8 cm 8 cm 8 cm 9:R8$ k3&M+&&k1>&w+&H3>U>&:B(YV\,-R0>.h>&(c:>*S>?*&M+&&k1,-Q>.E(I+3f>&F:+)•:*+& >?*&M+&&k1,-$ DE;Q0 A ER00 A E;00 A E^Q A 9:RR$)&(I.>?*/‚31&JK+)3LM+&A,-$ DEA EA EA EA 9:RO$m\>&`+>@:Y2+)Ej: DYn+)l]+)Ba( Dooo3&pS3q6r*3&M DoooYn+)l]+)   Ba( D3&pS3q6r$ DE* EA E; E8 9:RQ$&@+3f>&Y*3&=>A3&-+&+&@+3gh3* YJZ>$ DEA EF A EF%F[R4%FR4 EF%F#4%F[#4 9:R_$&S y +>@:3L* z ,K { (Y: | +)E &JK+)3L} { +&A>S | 3@ y 1+)&(~ y .,* { $ DEA EA EA EA 9:R^$&S3*.)(V>Dh „„% A Dh  A D4Y‰+)3&=>Y2+),- DEA EA EA EA 9:Re$a()(V3LW+-S>?*F3&MRFGQd&t+)+&ƒ&K+8F DE&t+)>U)(V3LW+-SEFA Q EFAQ E `(F 9:R#$(V3LW>?*/(T:3&=>F8[8F\[\83](FP^^B-\P8R,-$ DE^^00 E;0000 E^^00 E^Q00 9:O0$(T:3&=>DPNFGRN[FG8%Ba(FGRb046*:d&(L23)`+,-$ DEDP8FGQ EDP8F[Q EDP; EDPQ Š3 8 cm 8 cm 8 cm 8 cm _  _ R x x x+ > Ox > Ox < Qx > Qx < ; a R #x x− 8 % #4x x − 8 % #4x + ( ) ( ) ( ) ( ) F F 8F 8 F R 8 F ; F ; F R + = − + + − { } 6 0i e= − { } 6 0= ; 6 0i ^   = −     { } 6 0iR= ∈∈ AN AM BC MN = AB AM BC MN = AN AM MN BC = AB AM BC AN = ≥≤     !"# $ %&'()(*+,-./-(#01&234 567$eee 9:;$&S1&JK+)3LM+&A T1&JK+)3LM+&>U+)&(I.FP83&M.>U )(V3LW,-$ DE.P; E.P; E.P8 E.P8 9:8$23)`+/(T:3&=>8 A Ba(*b03*YJZ> DER* E^* ER* E^* 9:R$&S3*.)(V>DhDP;0>.hP#>.E!‚\Y(T.3L~+>]+&6*S>&SPR>.E!‚\Y(T. h3L~+>]+&D6*S>&SDPPO>.E`(ˆ,-)(*SY(T.>?*B-D *>U„„BM3LS+)3*.)(V>>U$ DEA EA EA EA 9:O$&S AB:t+)3](hYJ'+)>*SE(j3 DPe>.hP_>.Ekl-(YJ'+)>*S,-$ DEOhe>. E;0>. E;8>. E;Q>. 9:Q$)&(I.>?*/‚31&JK+)3LM+&A,-$ DEA EA EA EA 9:_$f+&)(V3LW/(T:3&=>A3*YJZ> DE80 E;e E88 ER0 9:^$&S y +>@:3L* z ,K { (Y: | +)E &JK+)3L} { +&A>S | 3@ y 1+)&(~ y .,* { $ DEA EA EA EA 9:e$&@+3f>&Y*3&=>A3&-+&+&@+3gh3* YJZ>$ DEA EF A EF%F[R4%FR4 EF%F#4%F[#4 9:#$&S3*.)(V>Dh „„% A Dh  A D4Y‰+)3&=>Y2+),- DEA EA EA EA 9:;0$a()(V3LW+-S>?*F3&MRFGQd&t+) +&ƒ&K+8F DE&t+)>U)(V3LW+-SEFA Q EFAQ E `(F 9:;;$a()(V3LW+-S>?*F3&M>•+3&=>A>U +)&€* DEFAA EFPA EFAA EFAA 9:;8$&S3*.)(V>D>U ,-3L:+)Y(T.>?* Di,-3L:+)Y(T.>?*Di/(j3 P80>.E&( YUYkl-(>]+&/C+)$ DE;0>. E80>. ER0>. EO0>. 9:;R$&S1&JK+)3LM+&A 8 R ; ; x m x x x − − + = − + aa Q 8 − CD CH CB CG = CD CH CB HG = BD GH BC HC = BD CH BC CG = ABC ∆ _  _ R x x x+ > Ox > Ox < Qx > Qx < O#$;#_8QE;_ + ( ) ( ) ( ) ( ) F F 8F 8 F R 8 F ; F ; F R + = − + + − { } 6 0i e= − { } 6 0= ; 6 0i ^   = −     { } 6 0iR= R #x x− 8 % #4x x − 8 % #4x + ∈∈ AN AM BC MN = AB AM BC MN = AN AM MN BC = AB AM BC AN = ≥≤ 8O −x 〉 8 ; 8 ; 〈 8 ; ≥ 8 ; 8 R ; ; x m x x x − − + = − + . cm 8 cm 8 cm 8 cm 9:R8$ k3& ;M+ &&k1>&w+&H3>U>&:B(YV,-R0>.h>&(c:>*S>?*& ;M+ &&k1,-Q>.E(I+3f>&F:+)•:*+&. Ev+)>V>)U>3LS+)3=)(V>/C+)R_00E E M+ &>&w+&H3>U&*(YJ'+)>&uS/C+)+&*:,-& ;M+ &B:t+)E 9:;Q$&S& ;M+ &3&*+)D%D„„4>U

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