MathDB
Pq=r

Source: Canada 2002

March 5, 2006
geometrycircumcircletrigonometryangle bisectorperpendicular bisectorgeometry unsolved

Problem Statement

Let Γ\Gamma be a circle with radius rr. Let AA and BB be distinct points on Γ\Gamma such that AB<3rAB < \sqrt{3}r. Let the circle with centre BB and radius ABAB meet Γ\Gamma again at CC. Let PP be the point inside Γ\Gamma such that triangle ABPABP is equilateral. Finally, let the line CPCP meet Γ\Gamma again at QQ. Prove that PQ=rPQ = r.
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