MathDB
Cute trapezoid geometry

Source: Kvant Magazine No. 8 2019 M2571

March 14, 2023
geometrytrapezoidKvant

Problem Statement

Let ABCDABCD be a trapezoid with AD∥BCAD \parallel BC, AD<BCAD < BC. Let EE be a point on the side ABAB and FF be point on the side CDCD. The circle (AEF)(AEF) intersects the segment ADAD again at A1A_1 and the circle (CEF)(CEF) intersects these segment BCBC again at C1C_1. Prove that the lines A1C1A_1 C_1, BDBD and EFEF are concurrent.
Proposed by A. Kuznetsov
Back to ProblemsView on AoPS