Classical tangents to the circumcircle
Source:
February 11, 2006
geometrycircumcirclegeometric transformationreflectionsimilar trianglesgeometry proposed
Problem Statement
Let be a circle with center , and let be a point outside the circle. Let the two tangents from the point to the circle meet this circle at the points and , respectively. Given a point on the circle which is different from the points and , let the line meet the perpendicular from the point to the line at .
Prove that the reflection of the point in the point lies on the line .