2 out of 3
Prove that the shaded area of the semicircle is equal to the area of the inner circle.
2 out of 3
2 out of 3
Take any rectangle ABCD such that AB > BC. The point P is on AB and Q is on CD. Show that there is exactly one position of P and Q such that APCQ is a rhombus.
2 out of 3
Can you prove Pythagoras' Theorem using enlargements and scale factors?
2 out of 3
A 10×10×10 cube is made from 27 2×2 cubes with corridors between them. Find the shortest route from one corner to the opposite corner.
2 out of 3
It is obvious that we can fit four circles of diameter 1 unit in a square of side 2 without overlapping. What is the smallest square into which we can fit 3 circles of diameter 1 unit?
2 out of 3
A rectangular piece of paper is folded. Can you work out one of the lengths in the diagram?
2 out of 3
A rectangular plank fits neatly inside a square frame when placed diagonally. What is the length of the plank?
2 out of 3
A fire-fighter needs to fill a bucket of water from the river and take it to a fire. What is the best point on the river bank for the fire-fighter to fill the bucket?
2 out of 3
How does the perimeter change when we fold this isosceles triangle in half?
