You may also like

problem icon

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

problem icon

Rotating Triangle

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

problem icon

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?

Semicircle Stack

Stage: 4 Short Challenge Level: Challenge Level:1

Three semicircles showing the rectangle and parts of a circle
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.

View the previous week's solution
View the current weekly problem