A scalene acute triangle ABC is drawn on the plane, in which BC is the longest side. Points P and D are constructed, the first inside ABC and the second outside, so that ∠ABC=∠CBD, ∠ACP=∠BCD and that the area of triangle ABC is equal to the area of quadrilateral BPCD. Prove that triangles BCD and ACP are similar. geometrysimilar trianglessimilarityequal angles