MathDB
concyclic circumcenters wanted, starting with 2 ext. tangent circles

Source: 2021 Dürer Math Competition Regional E+3 https://artofproblemsolving.com/community/c2773609_2021_

January 7, 2022
geometrycircumcircle

Problem Statement

Let k1k_1 and k2k_2 be two circles that are externally tangent at point CC. We have a point AA on k1k_1 and a point BB on k2k_2 such that CC is an interior point of segment ABAB. Let k3k_3 be a circle that passes through points AA and BB and intersects circles k1k_1 and k2k_2 another time at points MM and NN respectively. Let k4k_4 be the circumscribed circle of triangle CMNCMN. Prove that the centres of circles k1,k2,k3k_1, k_2, k_3 and k4k_4 all lie on the same circle.
Back to ProblemsView on AoPS