MathDB

G3

Part of 2015 IMO Shortlist

Problems(1)

Two lines meet on semicircle

Source: 2015 ISL G3

7/7/2016
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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