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2 points and 3 projections concyclic 2015-16 Dürer Round1 C1 D1

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December 5, 2022
geometryConcyclicDurer

Problem Statement

Let PP be an arbitrary point of the side line ABAB of the triangle ABCABC. Mark the perpendicular projection of PP on the side lines ACAC and BCBC as A1A_1 and B1B_1 respectively. Denote C1C_1 he foot of the alttiude starting from CC. Prove that the points A1A_1, B1B_1, C1C_1, CC and PP lie on a circle.
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