MathDB

2013 HMMT Geometry # 4

Source:

March 3, 2024

geometry

Problem Statement

Let

\omega_1

and

\omega_2

be circles with centers

O_1

and

O_2

, respectively, and radii

r_1

and

r_2

, respectively. Suppose that

O_2

is on

\omega_1

. Let

A

be one of the intersections of

\omega_1

and

\omega_2

, and

B

be one of the two intersections of line

O_1O_2

with

\omega_2

. If

AB = O_1A

, find all possible values of

\frac{r_1}{r_2}

.

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