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Cty TNHH MTV DWH Khang Vift Zau 5: Ta c6 AC = BD = 2a Gpi SO la duong cao va SO = h Trpn h$ true tga dp Oxyz cho: O(0;0;0), A(a;0;0), B(0;a;0), C(-a;0;0), D(0;-a;0), S(0;0;h) Cau 6: Khong mat tinh tong quat ta c6 the gia su: x > y > z Xethamso: f ( x ) = —H Xac djnh tarn va ban kinh m|it cau ngoai tiep hinh chop Do hinh chop S.ABCD la t i i giac deu (S):x^+y^+z^-2zoZ + d = iL ie uO nT hi Da iH oc 01 / h2-2znh + d = Xetf(y) = d = -a^ 2h Mat khac: a^+h^ 1 (l + y z ) ^ + —+ -zj y Ta a(2cosa-l) A Theo chUorng trinh chuan s/ = 2^cosa(l-cosa) /g ro Xac dinh tam va ban kinh mgt cau npi tiep hinh chop om j ( ; ; r ) , OJ = r c 2a\ ok ^S.ABCD - g S T p / V g A B C D ce bo SxQ = S ^ A B =4.isA.SB.sina = 2(a^ + h ^ ) s i n a w fa =>STP = S A B C D +SxQ =2(a^ + h ^ ) s i n a + 2a^ aJcosa(l-cosa) ww a./cosa(l-cosa) + sina-cosa + sina-cosa Tim a de mat cau ngoai tiep va npi tiep triing a^cosa(l - cosa) I = J o O I = OJo1 + sina-cosa (sina - cos a)(sin a - cosa +1) \2 (2 + z)'^ ,chu'ng minh dupe f (z) < 27 I I PHAN R I E N G Thi sinh chi dugc chpn lam mpt hai phan (phan A hoac B ) -cosa a •R= r,Ol 2^cosa(l-cosa) Ta c6: J e OS 1 + - + - (i+y+z)^- Xet f ( z ) = up SA.SB cos a = SA.SB > 0, x^ ^ y z , '"> Chung minh dup-c: f ( y ) < f ( l ) = + i l ( + z ) ' h^-a^ Zn =• x^yz suyra f ( x ) dongbiehva f ( x ) < f ( l ) = 'a2+d = A,S€(S): (x + y + z) xyz + ^2x^ - y z j ( y + z) Taco: f ' ( x ) = (x + y + z) nen I € OS =:i> l(0;0;Zo) + — a(2cosa-l) 2^cosa(l-cosa) Cau 7.a: ( C ) : (x - ) ^ + (y +1)^ = c6 tam l ( ; - l ) va ban kinh R = Gia su duong thSng qua P c6 vec to phap tuyen n(a;b)=>d:a(x-l) + b(y-3) = De d la tiep tuye'n ciia (C) thi khoang each t u tam I den d bang ban kinh: 3a - b - a - 3b a^+b^ •b(4a-3b) = 0: -2d: a ( x - l ) = > d : x - l = b = - i a : ^ d : a ( x - l ) + - a ( y - ) = 0=>d:3x + y - = 3 T a c : P I = 2V5, PE = PF = V P I ^ - = V - = Tam giac lEP dong dang voi IHF suy ra: — - — = — = ^ = Vs I H EH IE IF EP r2 = > I H - - ^ = -==,EH = - ^ = - L ^ P H = P I - I H = - - ^ = - ^ V5 V5 V5 V5 N/S V5 Vay I = J o a = 45° 242 243 fuyen ch