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JBMO 2016 No 1 - Lingkaran dalam trapesium dan lingkaran dalam segitiga

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Sebuah trapesium $ABCD$ ($AB//CD,AB>CD$) mempunyai lingkaran dalam. Lingkaran dalam segitiga $ABC$ menyinggung sisi $AB$ dan $AC$ berturut-turut di titik $M$ dan $N$. Buktikan titik pusat lingkaran dalam $ABCD$ berada di garis $MN$.

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