Let Γ be a circle with radius r. Let A and B be distinct points on Γ such that AB<3r. Let the circle with centre B and radius AB meet Γ again at C. Let P be the point inside Γ such that triangle ABP is equilateral. Finally, let the line CP meet Γ again at Q.
Prove that PQ=r. geometrycircumcircletrigonometryangle bisectorperpendicular bisectorgeometry unsolved