collinear wanted, circumcircle related
Source: 2017 Latvia BW TST P12
December 16, 2022
geometrycircumcirclecollinear
Problem Statement
A diameter is drawn for the circumscribed circle of an acute-angled triangle , an arbitrary point is chosen on the segment , the straight line intersects at point . The foot of the perpendicular drawn from on is , the tangent drawn to the circle through the point , intersects the straight line at . A point (different from ) is chosen on such that is tangent to . Prove that points , and lie on the same line.