Reflections

The centre of the larger circle is at the midpoint of one side of an equilateral triangle and the circle touches the other two sides of the triangle. A smaller circle touches the larger circle and two sides of the triangle. If the small circle has radius 1 unit find the radius of the larger circle.

In a snooker game the brown ball was on the lip of the pocket but it could not be hit directly as the black ball was in the way. How could it be potted by playing the white ball off a cushion?

Given that ABCD is a square, M is the mid point of AD and CP is perpendicular to MB with P on MB, prove DP = DC.

A moveable screen slides along a mirrored corridor towards a centrally placed light source. A ray of light from that source is directed towards a wall of the corridor, which it strikes at 45 degrees before being reflected across to the opposite wall and so on until it hits the screen.

Make a footprint pattern using only reflections.

When a strip has vertical symmetry there always seems to be a second place where a mirror line could go. Perhaps you can find a design that has only one mirror line across it. Or, if you thought that was impossible, could you explain why ?

Does changing the order of transformations always/sometimes/never produce the same transformation?

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 ?.

I am standing behind five pupils who are signalling a five-digit number to someone on the opposite side of the playground. What number is actually being signalled?

Can you find the time between 3 o'clock and 10 o'clock when my digital clock looks the same from both the front and back?