IMO 2015 Shortlist G3
Let ABC be a triangle with =C “ 900 , and let H be the foot of the altitude from C. A point D is chosen inside the trian...
Category: Geometry
Problem
Let ABC be a triangle with =C “ 900 , and let H be the foot of the altitude from C. A point D is chosen inside the triangle CBH so that CH bisects AD. Let P be the intersection point of the lines BD and CH. Let ω be the semicircle with diameter BD that meets the segment CB at an interior point. A line through P is tangent to ω at Q. Prove that the lines CQ and AD meet on ω. (Georgia)