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<CA_1B=90^o, symmetric points wrt lines- All-Russian MO 1999 Regional (R4) 8.6

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September 24, 2024
right angleperpendiculargeometry

Problem Statement

Given triangle ABCABC. Point A1A_1 is symmetric to vertex AA wrt line BCBC, and point C1C_1 is symmetric to vertex CC wrt line ABAB. Prove that if points A1A_1, BB and C1C_1 lie on the same line and C1B=2A1BC_1B = 2A_1B, then angle ∠CA1B\angle CA_1B is right.
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