MathDB
triangles $BTP$ and $DTQ$ are similar

Source: 2016 239 J2

October 11, 2020
geometry

Problem Statement

In a convex quadrilateral ABCDABCD rays ABAB and DCDC intersect at point PP, and rays BCBC and ADAD at point QQ. There is a point TT on the diagonal ACAC such that the triangles BTPBTP and DTQDTQ are similar, in that order. Prove that BDPQBD \Vert PQ.