MathDB
cyclic hexagon wanted, starting wih intersecting circles

Source: Dutch BxMO TST 2010 p4

August 3, 2019
hexagonCyclicgeometrycircles

Problem Statement

The two circles Γ1\Gamma_1 and Γ2\Gamma_2 intersect at PP and QQ. The common tangent that's on the same side as PP, intersects the circles at AA and BB,respectively. Let CC be the second intersection with Γ2\Gamma_2 of the tangent to Γ1\Gamma_1 at PP, and let DD be the second intersection with Γ1\Gamma_1 of the tangent to Γ2\Gamma_2 at QQ. Let EE be the intersection of APAP and BCBC, and let FF be the intersection of BPBP and ADAD. Let MM be the image of PP under point reflection with respect to the midpoint of ABAB. Prove that AMBEQFAMBEQF is a cyclic hexagon.
Back to ProblemsView on AoPS