You may also like

problem icon

Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

problem icon

Circles Ad Infinitum

A circle is inscribed in an equilateral triangle. Smaller circles touch it and the sides of the triangle, the process continuing indefinitely. What is the sum of the areas of all the circles?

problem icon

Golden Thoughts

Rectangle PQRS has X and Y on the edges. Triangles PQY, YRX and XSP have equal areas. Prove X and Y divide the sides of PQRS in the golden ratio.

Weekly Problem 37 - 2011

Challenge Level: Challenge Level:1

Ans 1:1

Let AB have length 3r. The distance moved by A is then the circumference of a semicircle radius 3r (3$\pi$r). C moves along a circle of radius 2r (2$\pi$r), followed by a semicircle of radius r ($\pi$r). The total distance moved by C is therefore also 3$\pi$r.


This problem is taken from the UKMT Mathematical Challenges.

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