MathDB

12

Part of 1997 Baltic Way

Problems(1)

Midpoint of AB is also the midpoint of YZ

Source: Baltic Way 1997

1/28/2011
Two circles C1\mathcal{C}_1 and C2\mathcal{C}_2 intersect in PP and QQ. A line through PP intersects C1\mathcal{C}_1 and C2\mathcal{C}_2 again at AA and BB, respectively, and XX is the midpoint of ABAB. The line through QQ and XX intersects C1C_1 and C2C_2 again at YY and ZZ, respectively. Prove that XX is the midpoint of YZYZ.
geometryparallelogramgeometry proposed