MathDB
Prove that CMN is tangent to S1 and S2

Source: All-Russian MO 2000

December 30, 2012
geometrycircumcircleRussia

Problem Statement

Let EE be a point on the median CDCD of a triangle ABCABC. The circle S1\mathcal S_1 passing through EE and touching ABAB at AA meets the side ACAC again at MM. The circle S2S_2 passing through EE and touching ABAB at BB meets the side BCBC at NN. Prove that the circumcircle of △CMN\triangle CMN is tangent to both S1\mathcal S_1 and S2\mathcal S_2.
Back to ProblemsView on AoPS