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JBMO Shortlist 2021 G2

Source: JBMO Shortlist 2021

July 2, 2022
JuniorBalkanshortlist2021geometryarcs

Problem Statement

Let PP be an interior point of the isosceles triangle ABCABC with A^=90∘\hat{A} = 90^{\circ}. If PAB^+PBC^+PCA^=90∘,\widehat{PAB} + \widehat{PBC} + \widehat{PCA} = 90^{\circ}, prove that AP⊥BCAP \perp BC.
Proposed by Mehmet Akif Yıldız, Turkey
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