### 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:

We contruct a new triangle as shown. Angle $x$ is equal to $90^\circ - (90^\circ - y) = y$, so the highlighted triangles are similar. Therefore $$p = 48 \times \frac{39}{52} = 36$$ $$q =20\times \frac{39}{52} = 15$$

The base is split $48 - q : q = 33 : 15 = 11 : 5$ and the ball falls a distance of $p + 20 = 36 + 20 = 56$.