MathDB

2022 Geo Div 1 P6

Source:

February 28, 2022

geometry

Problem Statement

Let

\Gamma_1

and

\Gamma_2

be two circles with radii

r_1

and

r_2,

respectively, where

r_1>r_2.

Suppose

\Gamma_1

and

\Gamma_2

intersect at two distinct points

A

and

\Gamma_2

A point

C

is selected on ray

\overrightarrow{AB},

past

B,

and the tangents to

\Gamma_1

and

\Gamma_2

from

C

are marked as points

P

and

Q,

respectively. Suppose that

\Gamma_2

passes through the center of

\Gamma_1

and that points

P, B, Q

are collinear in that order, with

PB=3

and

QB=2.

What is the length of

AB?

Proposed by Kyle Lee

Back to Problems View on AoPS