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equal angles

Source: Iranian third round 2015 geometry problem 3

September 10, 2015
geometrygeometric transformationreflection

Problem Statement

Let ABCABC be a triangle. consider an arbitrary point PP on the plain of △ABC\triangle ABC. Let R,QR,Q be the reflections of PP wrt AB,ACAB,AC respectively. Let RQ∩BC=TRQ\cap BC=T. Prove that ∠APB=∠APC\angle APB=\angle APC if and if only ∠APT=90∘\angle APT=90^{\circ}.
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