MathDB

circumcenter of BDF lies on circumcircle of AEO, ABC isosceles

Source: 2022 Grand Duchy of Lithuania, MC p3 (Baltic Way TST) https://artofproblemsolving.com/community/c1321893_grand

November 17, 2022

geometryConcyclicisosceles

Problem Statement

The center

O

of the circle

\omega

passing through the vertex

C

of the isosceles triangle

ABC

(

AB = AC

) is the interior point of the triangle

ABC

. This circle intersects segments

BC

and

AC

at points

D \ne C

and

E \ne C

, respectively, and the circumscribed circle

\Omega

of the triangle

AEO

at the point

F \ne E

. Prove that the center of the circumcircle of the triangle

BDF

lies on the circle

\Omega