IMO 2014 Shortlist G5
Let ABCD be a convex quadrilateral with =B “ =D “ 90˝ . Point H is the foot of the perpendicular from A to BD. The point...
Category: Geometry
Problem
Let ABCD be a convex quadrilateral with =B “ =D “ 90˝ . Point H is the foot of the perpendicular from A to BD. The points S and T are chosen on the sides AB and AD, respectively, in such a way that H lies inside triangle SCT and =SHC ´ =BSC “ 90˝ , =THC ´ =DTC “ 90˝ . Prove that the circumcircle of triangle SHT is tangent to the line BD. (Iran)