MathDB

2007.6

Part of Swiss NMO - geometry

Problems(1)

paralellogram wanted, 3 equal circles intersecing in pairs

Source: Switzerland - Swiss MO 2007 p6

7/18/2020
Three equal circles k1,k2,k3k_1, k_2, k_3 intersect non-tangentially at a point PP. Let AA and BB be the centers of circles k1k_1 and k2k_2. Let DD and CC be the intersection of k3k_3 with k1k_1 and k2k_2 respectively, which is different from PP. Show that ABCDABCD is a parallelogram.
geometryparallelogramequal circles