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<A=45^o, CD \perp AB, P\perp BC iff |AP| = |BC|.

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August 4, 2019
geometryperpendicularequal segments

Problem Statement

Let ABCABC be an acute triangle such that ∠BAC=45o\angle BAC = 45^o. Let DD a point on ABAB such that CD⊥ABCD \perp AB. Let PP be an internal point of the segment CDCD. Prove that AP⊥BCAP\perp BC if and only if ∣AP∣=∣BC∣|AP| = |BC|.
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