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reflections to get point inside triangle

Source: Mongolian MO 2007 Grade 11 P3

April 8, 2021
geometrygeometric transformationreflection

Problem Statement

Let PP be a point outside of the triangle ABCABC in the plane of ABCABC. Prove that by using reflections SABS_{AB}, SACS_{AC}, and SBCS_{BC} across the lines ABAB, ACAC, and BCBC one can shift point PP inside the triangle ABCABC.
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