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Circles Ad Infinitum

A circle is inscribed in an equilateral triangle. Smaller circles touch it and the sides of the triangle, the process continuing indefinitely. What is the sum of the areas of all the circles?

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Building Tetrahedra

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

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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?

Perception Versus Reality

Stage: 4 and 5 Challenge Level: Challenge Level:1
Well done to Martha from Kings Norton Girls' School who created a video response to this problem:

I created a video about the distribution of religions in England based on this task, however changed the question about 'how it should be' to 'how it was 50 years ago' as this was more suitable.

You can watch Martha's video on YouTube.