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OSN SMA 2017 No 7

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Diberikan jajargenjang $ABCD$. Titik $E$ dan titik $F$ dipilih berturut-turut pada sisi $BC$ dan $CD$ sedemikian rupa sehingga segitiga $ABE$ dan segitiga $BCF$ mempunyai luas yang sama. Diagonal $BD$ memotong $AE$ dan $AF$ berturut-turut di $M$ dan $N$. Buktikan terdapat segitiga yang panjang sisi-sisinya sama dengan $BM$, $MN$, dan $ND$.

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Hint 1:

Spoiler

CG:BG = CF:AB

 

Hint 2:

Spoiler

 

Dengan kesebangunan, nyatakan BM:BD dalam CG dan BG.

Analog untuk DN:BD.

 


 

Solusi:

Spoiler


Solusi saya bisa dicek di osn2017h2.pdf


 

 

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