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Adri

EGMO 2015 Hari 2 Soal 6.

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Misalkan  $H$ dan $G$ berturut-turut merupakan Orthocenter dan Centroid dari segitiga lancip $ \triangle ABC$ dengan $AB \neq AC$ . Garis $AG$ memotong  lingkaran luar  dari  $\triangle ABC$ di  $A$ dan $P$.  Misalkan $P^{\prime}$ adalah pencerminan dari $P$ di garis $BC$ . Buktikan bahwa $\angle CAB = 60^{ \circ}$ jika dan hanya jika $HG=GP^{\prime}$.


Edited by Adri

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