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Another quadrilateral in a circle

Source: APMO 2013, Problem 5

May 3, 2013
ratiogeometrycircumcirclegeometry proposed

Problem Statement

Let ABCDABCD be a quadrilateral inscribed in a circle ω\omega, and let PP be a point on the extension of ACAC such that PBPB and PDPD are tangent to ω\omega. The tangent at CC intersects PDPD at QQ and the line ADAD at RR. Let EE be the second point of intersection between AQAQ and ω\omega. Prove that BB, EE, RR are collinear.
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