MathDB
2 circles tangent to a third one , IMO SL 2020 variant

Source: P3 Francophone Math Olympiad Senior 2023

May 2, 2023
geometrytangent circles

Problem Statement

Let ABCDABCD be a convex quadrilateral, with ∡ABC>90∘\measuredangle ABC > 90^\circ, ∡CDA>90∘\measuredangle CDA > 90^\circ and ∡DAB=∡BCD\measuredangle DAB = \measuredangle BCD. Let EE, FF and GG be the reflections of AA with respect to the lines BCBC, CDCD and DBDB. Finally, let the line BDBD meet the line segment AEAE at a point KK, and the line segment AFAF at a point LL. Prove that the circumcircles of the triangles BEKBEK and DFLDFL are tangent to each other at GG.
Back to ProblemsView on AoPS