MathDB

G3

Part of 2017 Romanian Master of Mathematics Shortlist

Problems(1)

Hard geometry problem

Source: Romania 2017 IMO TST 3, problem 4

3/18/2018
Let ABCDABCD be a convex quadrilateral and let PP and QQ be variable points inside this quadrilateral so that ∠APB=∠CPD=∠AQB=∠CQD\angle APB=\angle CPD=\angle AQB=\angle CQD. Prove that the lines PQPQ obtained in this way all pass through a fixed point , or they are all parallel.
geometry