MathDB

2020 Geometry 6

Source:

February 2, 2020

geometry2020

Problem Statement

Two circles

\omega_A

and

\omega_B

have centers at points

A

and

B

respectively and intersect at points

P

and

Q

in such a way that

A

,

B

,

P

, and

Q

all lie on a common circle

\omega

. The tangent to

\omega

at

P

intersects

\omega_A

and

\omega_B

again at points

X

and

Y

respectively. Suppose

AB = 17

and

XY = 20

. Compute the sum of the radii of

\omega_A

and

\omega_B

.

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