### 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?

# Partly Circles

##### Stage: 4 Challenge Level:

Here are three problems involving circles.

Can you solve them?
Can you find relationships between the three problems?

Firstly :

Show that ab = cd

(where a, b, c, d are lengths)

Secondly:

These three circles are drawn so that they touch each other, and their centres are all on the line AB.

If CD is $8$ units in length, what is the area of the region shaded yellow?

Lastly:

If the area shaded yellow is equal to the area of the larger of the two blue circles, what is the relationship between the radii of the three circles?