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OSP SMA 2006 Bagian Kedua No 1

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Misalkan segitiga $ABC$ siku-siku di $B$. Garis tinggi dari $B$ memotong sisi $AC$ di titik $D$. Jika titik $E$ dan $F$ berturut-turut adalah titik tengah $BD$ dan $CD$, buktikan bahwa $AE \perp BF$.

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