Database Soal Olimpiade Matematika dari Seluruh Dunia
4. Sisi dari sebuah segiempat konveks diperpanjang sampai bertemu di titik . Misalkan titik tengah berturut-turut. Tentukan rasio luas terhadap .
Solusi:
Perhatikan bahwa dan jadi . Kita dapat . Tetapi
Jadi .
Written by Johan
18 Mei 2009 pada 16:07
Ditulis dalam olimpiade matematika
Ditandai dengan euklid, geometri, olimpiade matematika, rasio
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Kanada 1983
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OSK 2009
AIME 1983
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![[GDE]=\frac12[CDE]](http://l.wordpress.com/latex.php?latex=%5BGDE%5D%3D%5Cfrac12%5BCDE%5D&bg=fff&fg=1c1c1c&s=0 "[GDE]=\frac12[CDE]")
![[CHE]=\frac12[CDE]](http://l.wordpress.com/latex.php?latex=%5BCHE%5D%3D%5Cfrac12%5BCDE%5D&bg=fff&fg=1c1c1c&s=0 "[CHE]=\frac12[CDE]")
![[GDE]+[CHE]=[CDE]](http://l.wordpress.com/latex.php?latex=%5BGDE%5D%2B%5BCHE%5D%3D%5BCDE%5D&bg=fff&fg=1c1c1c&s=0 "[GDE]+[CHE]=[CDE]")
![[GHE]=[CHDG]](http://l.wordpress.com/latex.php?latex=%5BGHE%5D%3D%5BCHDG%5D&bg=fff&fg=1c1c1c&s=0 "[GHE]=[CHDG]")
![[CHDG]=[CHD]+[GHD]=\frac12[BCD]+\frac12[BGD]=\frac12[BCDG]=\frac12([BCG]+[GCD])=\frac12(\frac12[ABC]+\frac12[ACD])=\frac14[ABCD].](http://l.wordpress.com/latex.php?latex=%5BCHDG%5D%3D%5BCHD%5D%2B%5BGHD%5D%3D%5Cfrac12%5BBCD%5D%2B%5Cfrac12%5BBGD%5D%3D%5Cfrac12%5BBCDG%5D%3D%5Cfrac12%28%5BBCG%5D%2B%5BGCD%5D%29%3D%5Cfrac12%28%5Cfrac12%5BABC%5D%2B%5Cfrac12%5BACD%5D%29%3D%5Cfrac14%5BABCD%5D.&bg=fff&fg=1c1c1c&s=0 "[CHDG]=[CHD]+[GHD]=\frac12[BCD]+\frac12[BGD]=\frac12[BCDG]=\frac12([BCG]+[GCD])=\frac12(\frac12[ABC]+\frac12[ACD])=\frac14[ABCD].")
![[GHE]:[ABCD]=1:4](http://l.wordpress.com/latex.php?latex=%5BGHE%5D%3A%5BABCD%5D%3D1%3A4&bg=fff&fg=1c1c1c&s=0 "[GHE]:[ABCD]=1:4")
