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 is marked on the hypotenuse of a right triangle . The circle circumscribed around the triangle intersects the line at the point for the second time, and the circle circumscribed around the triangle intersects the line for the second time at the point . Prove that the line passes through the point .