MathDB

2

Part of 2006 Poland - Second Round

Problems(1)

Perpendicular lines plus two circles

Source:

2/25/2006
Point CC is a midpoint of ABAB. Circle o1o_1 which passes through AA and CC intersect circle o2o_2 which passes through BB and CC in two different points CC and DD. Point PP is a midpoint of arc ADAD of circle o1o_1 which doesn't contain CC. Point QQ is a midpoint of arc BDBD of circle o2o_2 which doesn't contain CC. Prove that PQ⊥CDPQ \perp CD.
geometrygeometric transformationreflectioncircumcircletrigonometrygeometry proposed