question 6
Source: iran tst 2014 third exam
May 21, 2014
geometrycircumcircletrigonometryratiosymmetrygeometry proposed
Problem Statement
The incircle of a non-isosceles triangle with the center touches the sides at .
let is a point on arc from circumcircle of triangle such that if are feet of perpendicular from on and is midpoint of we have .
prove that