MathDB

2021 Geo Div 2 P1

Source:

March 2, 2021

geometry

Problem Statement

Triangle

ABC

has a right angle at

A

,

AB=20

, and

AC=21

. Circles

\omega_A

,

\omega_B

, and

\omega_C

are centered at

A

,

B

, and

C

respectively and pass through the midpoint

M

of

\overline{BC}

.

\omega_A

and

\omega_B

intersect at

X\neq M

, and

\omega_A

and

\omega_C

intersect at

Y\neq M

. Find

XY

.
Proposed by Connor Gordon

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