2 tangents of different circles intersect on a line
Source: 2023 Czech-Polish-Slovak Match Junior, Team p4 CPSJ
May 5, 2024
geometrycollinear
Problem Statement
In triangle , the points and are the midpoints of the sides and , respectively. The bisectors of interior angles and intersect the line at points and , respectively. Let be the tangent to the circumscribed circle of the triangle passing through point , and be the tangent to the circumscribed circle of the triangle passing through point . Prove that the lines and intersect on line .