MathDB
collinear wanted, right triangle and 2 circles

Source: 2013 All-Ukrainain Correspondence MO of magazine ''In the World of Mathematics'', grades 5-12 p7

April 27, 2021
geometrycollinearright triangleUkraine Correspondence

Problem Statement

An arbitrary point DD is marked on the hypotenuse ABAB of a right triangle ABCABC. The circle circumscribed around the triangle ACDACD intersects the line BCBC at the point EE for the second time, and the circle circumscribed around the triangle BCDBCD intersects the line ACAC for the second time at the point FF. Prove that the line EFEF passes through the point DD.