MathDB
Two circles are congruent if tangent

Source: CSMO 2019 Grade 10 Problem 2

July 30, 2019
geometrycircumcircle

Problem Statement

Two circles Γ1\Gamma_1 and Γ2\Gamma_2 intersect at A,BA,B. Points C,DC,D lie on Γ1\Gamma_1, points E,FE,F lie on Γ2\Gamma_2 such that A,BA,B lies on segments CE,DFCE,DF respectively and segments CE,DFCE,DF do not intersect. Let CFCF meet Γ1,Γ2\Gamma_1,\Gamma_2 again at K,LK,L respectively, and DEDE meet Γ1,Γ2\Gamma_1,\Gamma_2 at M,NM,N respectively. If the circumcircles of △ALM\triangle ALM and △BKN\triangle BKN are tangent, prove that the radii of these two circles are equal.
Back to ProblemsView on AoPS