### 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?

### Tri-split

A point P is selected anywhere inside an equilateral triangle. What can you say about the sum of the perpendicular distances from P to the sides of the triangle? Can you prove your conjecture?

# Curvy Areas

##### Stage: 4 Challenge Level:
Suppose the radius of the smallest semicircle is $x$.
What are the radii of the other semicircles?
What areas can you work out, in terms of $x$ and $\pi$?