MathDB

Easy geo with circle

Source: Kvant Magazine No. 2 2023 M2735

April 19, 2023

geometrycircles

Problem Statement

Let

AB

be a diameter of the circle

\Omega

with center

O{}

. The points

C, D, X

and

Y{}

are chosen on

\Omega

so that the segments

CX

and

DX

intersect the segment

AB

at points symmetric with respect to

O{}

, and

XY\parallel AB

. Let the lines

AB{}

and

CD{}

intersect at the point

E

. Prove that the tangent to

\Omega

through

Y{}

passes through

E{}

.

Back to Problems View on AoPS