4

Part of 1987 Balkan MO

Problems(1)

two circles - classic and nice problem of Bulgaria

Source: bmo 1987

K_{1}

K_{2}

O_{1}

O_{2}

1

\sqrt{2}

respectively, intersect at

A

B

C

K_{2}

such that the midpoint of

AC

K_{1}

. Find the length of the segment

AC

O_{1}O_{2}=2

trigonometrygeometrysimilar trianglesgeometry proposed