I B'D tren day Vay goc tao bo
Ta CO he phaong trinh: trinh:
trinh:
trinh:
nen a(d - 2a) > 0 => d > 2a. Day la di^u kien d^ tinh duoc b, c. Day la di^u kien d^ tinh duoc b, c. 4. Goi f(x) = x' - dx + ad - 2a'
Co f(a) = - a' < 0, f(2a) = a (2a - d) < 0 (do d > 2a ) z:>a va 2a d trong khoang hai nghidm ciia (*) => dpcm. khoang hai nghidm ciia (*) => dpcm.
139. a) Ke OK 1 d thi OK = a va SK i. d theo dinh If ba dudng vuong goc => d 1 mp(KOS) ii>mp(S,d) ± mp (KOS). => d 1 mp(KOS) ii>mp(S,d) ± mp (KOS).
Tam giac vuong KAO cho:
OA = KO a
sma sin a 3 3sina
Tam giac vuong SAO cho: SA' = SO' + OA' o 25a' 64a' 25a' 64a'
9 sin'a sm a <»25 = 64sin'a + 9<=>
1 1
sin' a = — o sin a = — => a = 30' 4 2 b) Doan thang SO c6 dinh, E va b) Doan thang SO c6 dinh, E va F luon nhin SO dudi m<^t goc vu6ng nen E, F thuoc mat c^u ducmg kinh SO.
Mat khac E, F cung thu6c mp (S, d) c6' dinh nen E, F thuoc (S, d) c6' dinh nen E, F thuoc ducmg tron giao tuyen (C) ciia
mp (S,d) va mat ciu. Hinh 113
Ke OH ± SK va do (1) ndn OH ± mp (S, d) =i> H e mat cfiu (SO). Dao lai, lay m6t diem baft ki E G (C) (E ^ S va H). SE e mp (S, d) nen SE cat d lai, lay m6t diem baft ki E G (C) (E ^ S va H). SE e mp (S, d) nen SE cat d
Of A. Trong (P) ke ducmg thang vuong goc OA tai O, cat d tai B, SB cat (C)
tai F. Vi E, F e (C) nen E, F e mat cau (SO) ^ OE ± SA, OF 1 SB.
Kit luqn: Quy tich E, F la dudng tron (C), giao cua mat ci\x (SO) va mp
(S,d) trCr hai diem S, H. ^
c. Xdc dinh tdm I cua mat cdu ngogi tie'p tA dien SOAB: Vi A BAO la
tam giac vuong dinh O nen trung diem M ciia canh huyen AB each deu
ba dinh ciia A BAO. Tir M dung duofng thang A ± (P) tai O thi moi
diem tren A each deu cac dinh cua A BAO vi chiing c6 hinh chieu tren (P) bang nhau: MO = MA = MB. Tir trung diem J ciia SO dung mp (R) (P) bang nhau: MO = MA = MB. Tir trung diem J ciia SO dung mp (R) vuong goc SO, no cat A tai 1.1 thuoc mp trung true (R) nen I each deu S
va O, I € A nen I each deu O, A, B =:i> Ila tam mat cau ngoai tiep tir
dien SOAB.
10 cat SM tai G. Ta phai chiing minh G la trong tam A SAB.
That vay. Do A //SO (vi chiing cung vuong goc v6i (P) nen theo Talet, ta c6:
^ = ^ = l ^ G S = 2GM(dpcm). ' SO 2 y ,
140. Bai toan khong sai neu ta cho hinh cau va hinh non long vao nhau sao
cho chan ducmg cao hinh non triing \6'\p diem cua hinh cau va (P),
liJC nay tam hinh cau thuoc ducmg cao hinh non. (adsbygoogle = window.adsbygoogle || []).push({});
Hinh 114 la thiet dien qua true hinh non, cat hinh non theo mot thiet dien la tam giac can, cat hinh cau theo mot thiet dien la hinh tron Idn dien la tam giac can, cat hinh cau theo mot thiet dien la hinh tron Idn
(qua tam hinh cau), c6 ban kinh bang R.
Do (Q) // (P) => A'l //AB nen theo Talet ta c6: SI DC SH HA h - x IKi h - x IKi
h R A'l' = IJ.IH = (2R -x)x A'l' = IJ.IH = (2R -x)x
R