MathDB

locus of projections from the circumcenter - returns

Source: Sharygin Final 2024 8.6

August 2, 2024

geometrycircumcircleSharygin Geometry OlympiadSharygin 2024reflection

Problem Statement

A circle

\omega

touched lines

a

and

b

at points

A

and

B

respectively. An arbitrary tangent to the circle meets

a

and

b

X

and

Y

respectively. Points

X'

and

Y'

are the reflections of

X

and

Y

about

A

and

B

respectively. Find the locus of projections of the center of the circle to the lines

X'Y'