### Some(?) of the Parts

A circle touches the lines OA, OB and AB where OA and OB are perpendicular. Show that the diameter of the circle is equal to the perimeter of the triangle

### Rotating Triangle

What happens to the perimeter of triangle ABC as the two smaller circles change size and roll around inside the bigger circle?

### 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?

# Semi-detached

##### Stage: 4 Challenge Level:

In the diagram below, the blue square is inscribed in the semicircle, and the yellow square is inscribed in the circle.

The blue square has an area of $40$cm$^2$.

Can you find the area of the yellow square?