MathDB
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 ABCABC (AB=ACAB = AC). A straight line \ell is drawn through its vertex BB at a right angle with ABAB . On the straight line ACAC, an arbitrary point DD is taken, different from the vertices, and a straight line is drawn through it at a right angle with ACAC, intersecting \ell at the point FF. Prove that the center of the circle circumscribed around the triangle BCDBCD lies on the circumscribed circle of triangle ABDABD.