# Twin Incircles

**Geometry**Level 4

This new point \(D\) is a point such that the radius of the incircle of the triangle \(\triangle ACD\) is equal to the radius of the incircle of the triangle \(\triangle ABC\). If the ratio \(\frac{\overline{AD}}{\overline{CD}}\) can be expressed as \(\frac {x} {y}\), \(x\) and \(y\) being coprime, then find the value of \(x - y\)