Coke Machine

The coke machine in college takes 50 pence pieces. It also takes a certain foreign coin of traditional design...

Just Opposite

A and C are the opposite vertices of a square ABCD, and have coordinates (a,b) and (c,d), respectively. What are the coordinates of the vertices B and D? What is the area of the square?

Get Cross

A white cross is placed symmetrically in a red disc with the central square of side length sqrt 2 and the arms of the cross of length 1 unit. What is the area of the disc still showing?

Wedge on Wedge

Stage: 4 Challenge Level:

Two right-angled triangles are connected together as part of a structure.

The green triangle has side lengths of 65, 52, and 39 cm and the blue triangle has side lengths of 52, 48, and 20 cm.

An object is dropped from the top of the green triangle, where does it pass the base of the blue triangle?

In what proportion is the blue base split and how far has the object fallen?

This problem does not require a calculator or any special formula.