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CNCM Online R2P7

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August 8, 2020
CNCMProblem Discussion

Problem Statement

A circle is centered at point OO in the plane. Distinct pairs of points A,BA, B and C,DC, D are diametrically opposite on this circle. Point PP is chosen on line segment ADAD such that line BPBP hits the circle again at MM and line ACAC at XX such that MM is the midpoint of PXPX. Now, the point Y≠XY \neq X is taken for BX=BY,CD∥XYBX = BY, CD \parallel XY. IF ∠PYB=10∘\angle PYB = 10^{\circ}, find the measure of ∠XCM\angle XCM.
Proposed by Albert Wang (awang11)
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