MathDB
Classical tangents to the circumcircle

Source:

February 11, 2006
geometrycircumcirclegeometric transformationreflectionsimilar trianglesgeometry proposed

Problem Statement

Let C\mathcal{C} be a circle with center OO, and let AA be a point outside the circle. Let the two tangents from the point AA to the circle C\mathcal{C} meet this circle at the points SS and TT, respectively. Given a point MM on the circle C\mathcal{C} which is different from the points SS and TT, let the line MAMA meet the perpendicular from the point SS to the line MOMO at PP. Prove that the reflection of the point SS in the point PP lies on the line MTMT.