10.5

Part of 2005 Sharygin Geometry Olympiad

Problems(1)

computational with intersecting circles, tangents from a point of one circle

Source: Sharygin 2005 finals 10.5

Two circles of radius

1

intersect at points

X, Y

, the distance between which is also equal to

1

C

of one circle, tangents

CA, CB

are drawn to the other. Line

CB

will cross the first circle a second time at point

A'

. Find the distance

AA'

geomatrydistancecirclesTangentsgeometry