MathDB

2022 Team 3

Source:

March 14, 2022

geometry

Problem Statement

Let triangle

ABC

be an acute triangle with circumcircle

\Gamma

. Let

X

and

Y

be the midpoints of minor arcs

AB

and

AC

of

\Gamma

, respectively. If line

XY

is tangent to the incircle of triangle

ABC

and the radius of

\Gamma

is

R

, find, with proof, the value of

XY

in terms of

R

.

Back to Problems View on AoPS