### Rotating Triangle

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

### Intersecting Circles

Three circles have a maximum of six intersections with each other. What is the maximum number of intersections that a hundred circles could have?

### Square Pegs

Which is a better fit, a square peg in a round hole or a round peg in a square hole?

# Central Distance

##### Stage: 3 Short Challenge Level:

The diameter of the circles is 5cm, so the radius of the circles is 2.5cm.

Each centre is 2.5cm from the nearest side of the rectangle.

So the distance between them is (9 - (2 x 2.5))cm = 4cm

This problem is taken from the UKMT Mathematical Challenges.