Consider a right angled triangle $$ABC$$ with right angle at $$A$$. The radius of its incircle is $$r$$. Radius of the circle drawn touching the line segments $$AB$$, $$AC$$ and the incircle of triangle $$ABC$$ is __________

PLACEHOLDER ANSWER - the answer is an expression in $$r$$. Both circles touch $$AB$$ and $$AC$$, so their centres lie on the bisector of the right angle at $$A$$, at distances $$r\sqrt{2}$$ and $$s\sqrt{2}$$ from $$A$$. As they touch, $$r\sqrt{2} - s\sqrt{2} = r + s$$, so $$s = \frac{\sqrt{2} - 1}{\sqrt{2} + 1}r = (3 - 2\sqrt{2})r$$.