MathDB

Find the locus of circumcenter.

Source: Mongolian TST 2008 day4 problem3

May 28, 2008

geometrycircumcirclepower of a pointradical axisgeometry proposed

Problem Statement

Let

\Omega

is circle with radius

R

and center

O

. Let

\omega

is a circle inside of the

\Omega

with center

I

radius

r

.

X

is variable point of

\omega

and tangent line of

\omega

pass through

X

intersect the circle

\Omega

at points

A,B

. A line pass through

X

perpendicular with

AI

intersect

\omega

at

Y

distinct with

X

.Let point

C

is symmetric to the point

I

with respect to the line

XY

.Find the locus of circumcenter of triangle

ABC

when

X

varies on

\omega

Back to Problems View on AoPS