collinear wanted, starting with right isosceles triangle
Source: III Soros Olympiad 1996-97 R2 9.6 https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics
May 31, 2024
geometrycollinear
Problem Statement
Let be an isosceles right triangle with hypotenuse , be some point in the plane such that and point inside the triangle . We construct two rays with a start in , intersecting and and perpendicular to them. On the first one, intersecting , we will plot the segment , and on the second one - . Prove that points , and lie on the same line.