MathDB

Circle Incident

Source: 2016 AIME I #15

March 4, 2016

2016 AIME IcirclesAIME

Problem Statement

Circles

\omega_1

and

\omega_2

intersect at points

X

and

Y

. Line

\ell

is tangent to

\omega_1

and

\omega_2

at

A

and

B

, respectively, with line

AB

closer to point

X

than to

\omega_2

. Circle

\omega

passes through

A

and

B

intersecting

\omega_1

again at

D \neq A

and intersecting

\omega_2

again at

C \neq B

. The three points

C

,

Y

,

D

are collinear,

XC = 67

,

XY = 47

, and

XD = 37

. Find

AB^2

.

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