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similar triangles wanted, <ABC = <CBD, <ACP=<BCD, (ABC)=(BPCD)

Source: Mathematics Regional Olympiad of Mexico West 2018 P3

September 8, 2022
geometrysimilar trianglessimilarityequal angles

Problem Statement

A scalene acute triangle ABCABC is drawn on the plane, in which BCBC is the longest side. Points PP and DD are constructed, the first inside ABCABC and the second outside, so that ∠ABC=∠CBD\angle ABC = \angle CBD, ∠ACP=∠BCD\angle ACP = \angle BCD and that the area of triangle ABCABC is equal to the area of quadrilateral BPCDBPCD. Prove that triangles BCDBCD and ACPACP are similar.
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