A M M A 1 = S A M B S M B A 1 = S A M C S M C A 1 = S A M B + S A M C S B M C \frac{AM}{MA_1}=\frac{S_{AMB}}{S_{MBA_1}}=\frac{S_{AMC}}{S_{MCA_1}}=\frac{S_{AMB}+S_{AMC}}{S_{BMC}} M A 1 A M = S M B A 1 S A M B = S M C A 1 S A M C = S B M C S A M B + S A M C Tương tự B M M B 1 = S A M B + S B M C S A M C \frac{BM}{MB_1}=\frac{S_{AMB}+S_{BMC}}{S_{AMC}} M B 1 B M = S A M C S A M B + S B M C C M M C 1 = S A M C + S B M C S A M B \frac{CM}{MC_1}=\frac{S_{AMC}+S_{BMC}}{S_{AMB}} M C 1 C M = S A M B S A M C + S B M C A M M A 1 + B M M B 1 + C M M C 1 \frac{AM}{MA_1}+\frac{BM}{MB_1}+\frac{CM}{MC_1} M A 1 A M + M B 1 B M + M C 1 C M = S A M B + S A M C S B M C + S A M C + S B M C S A M B + S A M C + S B M C S A M B =\frac{S_{AMB}+S_{AMC}}{S_{BMC}}+\frac{S_{AMC}+S_{BMC}}{S_{AMB}}+\frac{S_{AMC}+S_{BMC}}{S_{AMB}} = S B M C S A M B + S A M C + S A M B S A M C + S B M C + S A M B S A M C + S B M C = ( S A M B + S B M C + S A M C ) ( 1 S A M B + 1 S B M C + 1 S A M C ) − 3 =(S_{AMB}+S_{BMC}+S_{AMC})(\frac{1}{S_{AMB}}+ \frac{1}{S_{BMC}}+ \frac{1}{S_{AMC}})-3 = ( S A M B + S B M C + S A M C ) ( S A M B 1 + S B M C 1 + S A M C 1 ) − 3 9 − 3 = 6 9-3=6 9 − 3 = 6 A M M A 1 . B M M B 1 . C M M C 1 \frac{AM}{MA_1}.\frac{BM}{MB_1}.\frac{CM}{MC_1} M A 1 A M . M B 1 B M . M C 1 C M = ( S A M B + S B M C ) ( S B M C + S A M C ) ( S A M C + S A M B ) S A M B . S B M C . S A M C =\frac{(S_{AMB}+S_{BMC})(S_{BMC}+S_{AMC})(S_{AMC}+S_{AMB})}{S_{AMB}.S_{BMC}.S_{AMC}} = S A M B . S B M C . S A M C ( S A M B + S B M C ) ( S B M C + S A M C ) ( S A M C + S A M B ) 2 S A M B . S B M C . 2 S B M C . S A M C . 2 S A M C . S A M B S A M B . S B M C . S A M C \frac{2\sqrt{S_{AMB}.S_{BMC}}.2\sqrt{S_{BMC}.S_{AMC}}.2\sqrt{S_{AMC}.S_{AMB}}}{S_{AMB}.S_{BMC}.S_{AMC}} S A M B . S B M C . S A M C 2 S A M B . S B M C . 2 S B M C . S A M C . 2 S A M C . S A M B = 8 S A M B . S B M C . S A M C S A M B . S B M C . S A M C = 8 =\frac{8S_{AMB}.S_{BMC}.S_{AMC}}{S_{AMB}.S_{BMC}.S_{AMC}}=8 = S A M B . S B M C . S A M C 8 S A M B . S B M C . S A M C = 8
Last edited by a moderator: 2 Tháng chín 2014
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