Let ABC be an acute scalene triangle. Its C-excircle tangent to the segment AB meets
AB at point M and the extension of BC beyond B at point N. Analogously, its B-excircle
tangent to the segment AC meets AC at point P and the extension of BC beyond C at point
Q. Denote by A1 the intersection point of the lines MN and PQ, and let A2 be defined as the
point, symmetric to A with respect to A1. Define the points B2 and C2, analogously. Prove
that △ABC is similar to △A2B2C2.
Balkanshortlist2021geometryexcirclesimilar triangles