MathDB

2008.11

Part of Ukraine Correspondence MO - geometry

Problems(1)

concyclic wanted, starting with a #, a circle and a perpendicular

Source: 2008 All-Ukrainian Correspondence MO of magazine ''In the World of Mathematics'', grades 5-12 p11

4/28/2021
Let ABCDABCD be a parallelogram. A circle with diameter ACAC intersects line BDBD at points PP and QQ. The perpendicular on ACAC passing through point CC, intersects lines ABAB and ADAD at points XX and YY, respectively. Prove that the points P,Q,XP, Q, X and YY lie on the same circle.
geometryparallelogramConcyclicUkraine Correspondence