### Pericut

Two semicircle sit on the diameter of a semicircle centre O of twice their radius. Lines through O divide the perimeter into two parts. What can you say about the lengths of these two parts?

### Circumspection

M is any point on the line AB. Squares of side length AM and MB are constructed and their circumcircles intersect at P (and M). Prove that the lines AD and BE produced pass through P.

A circle is inscribed in a triangle which has side lengths of $8, 15$ and $17 \; \text{cm}$.
Can you adapt your method to find the radius of a circle inscribed in any right-angled triangle $ABC$?