MathDB

2016 Team #15

Source:

August 17, 2022

2016team test

Problem Statement

Circles

\omega_1

and

\omega_2

have radii

r_1<r_2

respectively and intersect at distinct points

X

and

Y

. The common external tangents intersect at point

Z

. The common tangent closer to

X

touches

\omega_1

and

\omega_2

at

P

and

Q

respectively. Line

ZX

intersects

\omega_1

and

\omega_2

again at points

R

and

XY=12

and lines

RP

and

SQ

intersect again at point

T

. If

XT=8

,

XZ=15

, and

XY=12

, then what is

\tfrac{r_1}{r_2}

?

Back to Problems View on AoPS