circumcenter of (BCD) lies on (ABD), AB=AC
Source: VI Soros Olympiad 1990-00 R3 11.4 https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics
May 28, 2024
geometryConcyclic
Problem Statement
Given isosceles triangle (). A straight line is drawn through its vertex at a right angle with . On the straight line , an arbitrary point is taken, different from the vertices, and a straight line is drawn through it at a right angle with , intersecting at the point . Prove that the center of the circle circumscribed around the triangle lies on the circumscribed circle of triangle .