MathDB

two circles - classic and nice problem of Bulgaria

Source: bmo 1987

April 23, 2007

trigonometrygeometrysimilar trianglesgeometry proposed

Problem Statement

Two circles

K_{1}

and

K_{2}

, centered at

O_{1}

and

O_{2}

with radii

1

and

\sqrt{2}

respectively, intersect at

A

and

B

. Let

C

be a point on

K_{2}

such that the midpoint of

AC

lies on

K_{1}

. Find the length of the segment

AC

O_{1}O_{2}=2