Let O denote the circumcentre of an acute-angled triangle ABC. Let point P on side AB be such that ∠BOP=∠ABC, and let point Q on side AC be such that ∠COQ=∠ACB. Prove that the reflection of BC in the line PQ is tangent to the circumcircle of triangle APQ. geometrycircumcirclegeometric transformationreflectionsymmetrytrigonometryrhombus