In a triangle
we have
A circle which is internally tangent with the circumscribed circle of the triangle is also tangent to the sides
in the points
respectively
Prove that the midpoint of
is the center of the inscribed circle of the triangle
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In a triangle $ABC$ we have $AB = AC.$ A circle which is internally tangent with the circumscribed circle of the triangle is also tangent to the sides $AB, AC$ in the points $P,$ respectively $Q.$ Prove that the midpoint of $PQ$ is the center of the inscribed circle of the triangle $ABC.$
Školjka