You may also like

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.

problem icon

Building Tetrahedra

Can you make a tetrahedron whose faces all have the same perimeter?

problem icon

Ladder and Cube

A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?

Circled Corners

Stage: 4 Short Challenge Level: Challenge Level:2 Challenge Level:2

The three angles of the triangle add to $180^{\circ}$, so the combined area of the three sectors of the circles that are inside the triangle add up to half a circle with area:
$\frac{1}{2} \times \pi \times 2^2 = \frac {4\pi}{2}= 2\pi$. 
So the grey area is $(80- 2\pi) cm^2$.

This problem is taken from the UKMT Mathematical Challenges.
View the archive of all weekly problems grouped by curriculum topic

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