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<PCB =? ABCD rectangle 1x2, MBP equilateral. AM=//MD

Source: 2022 NZMO - New Zealand Maths Olympiad Round 1 p1

October 9, 2022
geometryrectangleEquilateralangles

Problem Statement

ABCDABCD is a rectangle with side lengths AB=CD=1AB = CD = 1 and BC=DA=2BC = DA = 2. Let M M be the midpoint of ADAD. Point PP lies on the opposite side of line MBMB to AA, such that triangle MBPMBP is equilateral. Find the value of ∠PCB\angle PCB.
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