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2022 MMATHS Team Online p7 - 3 right angles and midpoint arc

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October 1, 2023
geometryMMATHS

Problem Statement

△ABC\vartriangle ABC satisfies AB=16AB = 16, BC=30BC = 30, and ∠ABC=90o\angle ABC = 90^o. On the circumcircle of △ABC\vartriangle ABC, let PP be the midpoint of arc ACAC not containing BB, and let XX and YY lie on lines ABAB and BCBC, respectively, with PX⊥ABPX \perp AB and PY⊥BCPY \perp BC. Find XY2XY^2.
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