MathDB
Two exsimilicenters in a trapezoid

Source: All-Russian MO 2023 Final stage 9.7/10.7

April 23, 2023
geometrytrapezoid

Problem Statement

Given a trapezoid ABCDABCD, in which AD∥BCAD \parallel BC, and rays ABAB and DCDC intersect at point GG. The common external tangents to the circles (ABC),(ACD)(ABC), (ACD) intersect at point EE. The common external tangents to circles (ABD),(CBD)(ABD), (CBD) meet at FF. Prove that the points E,FE, F and GG are collinear.
Back to ProblemsView on AoPS