MathDB

Consider a circle of radius

4

with center

O_1

, a circle of radius

2

with center

O_2

that lies on the circumference of circle

O_1

, and a circle of radius

1

with center

O_3

that lies on the circumference of circle

O_2

. The centers of the circle are collinear in the order

O_1

O_2

O_3

. Let

A

be a point of intersection of circles

O_1

and

O_2

and

B

be a point of intersection of circles

O_2

and

O_3

such that

A

and

B

lie on the same semicircle of

O_2

. Compute the length of

AB

Problem Statement