Problem

Source: Sharygin 2005 finals 10.5

Tags: geomatry, distance, circles, Tangents, geometry



Two circles of radius $1$ intersect at points $X, Y$, the distance between which is also equal to $1$. From point $C$ 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 $AA'$.