MathDB
Two lines meet on semicircle

Source: 2015 ISL G3

July 7, 2016
geometryIMO Shortlist

Problem Statement

Let ABCABC be a triangle with ∠C=90∘\angle{C} = 90^{\circ}, and let HH be the foot of the altitude from CC. A point DD is chosen inside the triangle CBHCBH so that CHCH bisects ADAD. Let PP be the intersection point of the lines BDBD and CHCH. Let ω\omega be the semicircle with diameter BDBD that meets the segment CBCB at an interior point. A line through PP is tangent to ω\omega at QQ. Prove that the lines CQCQ and ADAD meet on ω\omega.
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