MathDB

2021 USMCA National Championship #29

Source:

May 9, 2021

Problem Statement

Three circles

\Gamma_A, \Gamma_B, \Gamma_C

are externally tangent. The circles are centered at

A, B, C

and have radii

4, 5, 6

respectively. Circles

\Gamma_B

and

\Gamma_C

meet at

D

, circles

\Gamma_C

and

\Gamma_A

meet at

E

, and circles

\Gamma_A

and

\Gamma_B

meet at

F

. Let

GH

be a common external tangent of

\Gamma_B

and

\Gamma_C

on the opposite side of

BC

as

EF

, with

G

on

\Gamma_B

and

H

on

\Gamma_C

. Lines

FG

and

EH

meet at

K

. Point

L

is on

\Gamma_A

such that

\angle DLK = 90^\circ

. Compute

\frac{LG}{LH}

.

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