Given a right triangle ABC with ∠C=90o. On its hypotenuse AB is arbitrary mark the pointP. The point Q is symmetric to the point P wrt AC. Let the lines PQ and BQ intersect AC at points O and R respectively. Denote by S the foot of the perpendicular from the point R on the line AB (S=P), and let T be the intersection point of lines OS and BR. Prove that R is the center of the circle inscribed in the triangle CST. geometryincenterright triangleChampions Tournament