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equal segments wanted starting with an isosceles and right triangle

Source: Tuymaada Junior 2006 p1

May 12, 2019
geometryright triangleisoscelesequal segments

Problem Statement

On the equal AC AC and BC BC of an isosceles right triangle ABC ABC , points D D and E E are marked respectively, so that CD=CE CD = CE . Perpendiculars on the straight line AE AE , passing through the points C C and D D , intersect the side AB AB at the points P P and Q Q .Prove that BP=PQ BP = PQ .
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