MathDB
Excenter of isosceles triangle

Source: Turkey TST 1989 - P6

September 11, 2013
geometrycircumcirclegeometric transformationhomothetygeometry proposed

Problem Statement

The circle, which is tangent to the circumcircle of isosceles triangle ABCABC (AB=ACAB=AC), is tangent ABAB and ACAC at PP and QQ, respectively. Prove that the midpoint II of the segment PQPQ is the center of the excircle (which is tangent to BCBC) of the triangle .