MathDB

Variable chord tangent to a circle

Source: Kvant Magazine No. 11-12 2023 M2773

March 16, 2024

geometryFixed point

Problem Statement

The circle

\omega

lies inside the circle

\Omega

and touches it internally at

T.

Let

XY{}

be a variable chord of the circle

\Omega

touching

\omega.

Denote by

X'

and

Y'

the midpoints of the arcs

TY{}

and

TX{}

which do not contain

X{}

and

Y{}

respectively. Prove that all possible lines

X'Y'

pass through a fixed point.
Proposed by F. Petrov

Back to Problems View on AoPS