### 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?

# Weekly Problem 19 - 2006

##### Stage: 3 Challenge Level:

The shaded area may be divided into a $2 \times 1$ rectangle plus a semicircle plus two quarter circles (all of radius $1$). Hence the total area is that of the rectangle plus a circle of radius $1$. Making $2 + \pi$

This problem is taken from the UKMT Mathematical Challenges.

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