MathDB
a problem about ABD and ACD having equal in-radii

Source: romanian tst 2 - 2007 , problem 2

April 15, 2007
geometrycircumcirclegeometry proposed

Problem Statement

Let ABCABC be a triangle, EE and FF the points where the incircle and AA-excircle touch ABAB, and DD the point on BCBC such that the triangles ABDABD and ACDACD have equal in-radii. The lines DBDB and DEDE intersect the circumcircle of triangle ADFADF again in the points XX and YY. Prove that XY∥ABXY\parallel AB if and only if AB=ACAB=AC.
Back to ProblemsView on AoPS