MathDB

2017.11

Part of Ukraine Correspondence MO - geometry

Problems(1)

exists circle tangent to 4 circumcircles, #, <APB+<CPD=<BPC+<APD

Source: 2017 All-Ukrainian Correspondence MO, grades 5-12 p11

4/29/2021
Inside the parallelogram ABCDABCD, choose a point PP such that ∠APB+∠CPD=∠BPC+∠APD\angle APB+ \angle CPD= \angle BPC+ \angle APD. Prove that there exists a circle tangent to each of the circles circumscribed around the triangles APBAPB, BPCBPC, CPDCPD and APDAPD.
geometrytangent circlesparallelogramUkraine Correspondence