MathDB
Parallelogram geo

Source: All-Russian 2022 10.7

April 20, 2022
geometrytangentAll Russian Olympiadparallelogram

Problem Statement

Point EE is marked on side BCBC of parallelogram ABCDABCD, and on the side ADAD - point FF so that the circumscribed circle of ABEABE is tangent to line segment CFCF. Prove that the circumcircle of triangle CDFCDF is tangent to line AEAE.