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Radical center of Five circles

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

March 31, 2019
geometrygeometry proposed

Problem Statement

Given a convex pentagon ABCDE. ABCDE. Let A1 A_1 be the intersection of BD BD with CE CE and define B1,C1,D1,E1 B_1, C_1, D_1, E_1 similarly, A2 A_2 be the second intersection of ⊙(ABD1),⊙(AEC1) \odot (ABD_1),\odot (AEC_1) and define B2,C2,D2,E2 B_2, C_2, D_2, E_2 similarly. Prove that AA2,BB2,CC2,DD2,EE2 AA_2, BB_2, CC_2, DD_2, EE_2 are concurrent.
Proposed by Telv Cohl
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