Problem

Source: 2019 Taiwan TST Round 1, Quiz 3, Problem 2

Tags: geometry, geometry proposed



Given a convex pentagon $ ABCDE. $ Let $ A_1 $ be the intersection of $ BD $ with $ CE $ and define $ B_1, C_1, D_1, E_1 $ similarly, $ A_2 $ be the second intersection of $ \odot (ABD_1),\odot (AEC_1) $ and define $ B_2, C_2, D_2, E_2 $ similarly. Prove that $ AA_2, BB_2, CC_2, DD_2, EE_2 $ are concurrent. Proposed by Telv Cohl