MathDB
Inmo 2015

Source: inmo 2015 #1

February 1, 2015
geometryincentercircumcircletrigonometry

Problem Statement

Let ABCABC be a right-angled triangle with ∠B=90∘\angle{B}=90^{\circ}. Let BDBD is the altitude from BB on ACAC. Let P,QP,Q and II be the incenters of triangles ABD,CBDABD,CBD and ABCABC respectively.Show that circumcenter of triangle PIQPIQ lie on the hypotenuse ACAC.
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