A circle touches the sides $AC$ and $AB$ of the triangle $ABC $ at the points ${{B}_ {1}} $ and ${{C}_ {1}}$ respectively. The segments $B {{B} _ {1}} $ and $C {{C} _ {1}}$ are equal. Prove that the triangle $ABC $ is isosceles. (Timoshkevich Taras)
Source:
Tags: geometry, isosceles, circle
A circle touches the sides $AC$ and $AB$ of the triangle $ABC $ at the points ${{B}_ {1}} $ and ${{C}_ {1}}$ respectively. The segments $B {{B} _ {1}} $ and $C {{C} _ {1}}$ are equal. Prove that the triangle $ABC $ is isosceles. (Timoshkevich Taras)