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<BZC =90^o wanted, touchpoints with incircle, _|_ bisector

Source: Indonesia INAMO Shortlist 2010 G2

August 27, 2021
geometryincircleright angle

Problem Statement

Given an acute triangle ABCABC. The inscribed circle of triangle ABCABC is tangent to ABAB and ACAC at XX and YY respectively. Let CHCH be the altitude. The perpendicular bisector of the segment CHCH intersects the line XYXY at ZZ. Prove that ∠BZC=90o.\angle BZC = 90^o.
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