D eA Ih so nguyen thi j^— phdi Ik so nguyen
b) Bai toan phy:
^ , , . , V (x + y + z +1)^ ^. - Chffng minh r^ng — + — + — + — ^ -^^ — vdi p, q, r, s > 0 ^ p q r s p + q + r + s 2 2 2 Chffng minh: D§ d^ng chffng minh dffdc — + > p q p + q y 2 -2 Do vay c6 — + — + — + X - y " . z ' , r_ ^ (X + yY ^ ( z + t)^ ^ ( x + y + z + t)^ p + q r + s
Ap dung bai toan phu ta c6: 1 1 1
+ + p + q + r + s p + q + r + s 1 a + b b + c c + a 2yfs^ ,2 + • + c^(a + b) â(b + c) b^(c + a) ^2 2abc (a + b + c + yfabc^ (a + b + c + %/abc)^ c^(a + b) + â(b + c) + b^(c + a) + 2abc (a + b)(b + c)(c + a)
Bai 4. Qua P ve dffcJng thing song A
song vdi BC c^t A M , A N , AClan \ ^ P ^ ^ ^ l / / K '
Iffdt 3 I , K, Ẹ Goi H \h giao diem
cua PN va AC. ^' Chffng minh dffdc I la trung diem
cua PẸ
AAPH can tai Ạ IN la dffcJng trung binh cua tam gidc PEH.
Tff giac lECN Ik hinh bmh hanh. VI vay NC = IE = PI
Taco NQ M N M N M I NK => QK // AP
PQ PI NC A I AK
Nen KQ 1 OP. AOPK c6 PN, KQ la hai dff5ng cao c^t nhau tai Q. Do vay c6 Q O 1 P K . Vay Q O 1 B C
Bai 5. Ve dffdng kinh EF cua dffcfng o-6n (O). Goi H 1^ giao diem cua AB va DF, ADF = 90" (Goc noi tiep ch^n nffa dffcfng tr6n)
DE // AB, DF 1 D E => DF 1 AB.
Ta CO NCM = MED (sole trong v^ DE
MED = MDC (He qua g6c tao bdi tia tiep tuyen va day).
Nen NCM = MDC .
NC N M ANCM ^ ANDC ANCM ^ ANDC
ND NC CH.CO = CM.CE = CD' CH.CO = CM.CE = CD'
Tff gidc MEOH npi tiep => CHM = MEF = M D H A N H M ' ^ ANDH(g.g) NH N M
^uygii giui ue iiuut M im vau lup lU ua llliyil Bae, I rung, l\lam mOn loan _ Nguyen Dijfe Tan
NC^ = N H ' => NC = NH.
Ta cung c6 CA + CB = CO - OA + CO + OB = 2CO
BC + AC 2CO 2CO 2CO 2 2 1 1