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Rotating Triangle

What happens to the perimeter of triangle ABC as the two smaller circles change size and roll around inside the bigger circle?

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Two semicircle sit on the diameter of a semicircle centre O of twice their radius. Lines through O divide the perimeter into two parts. What can you say about the lengths of these two parts?

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A point P is selected anywhere inside an equilateral triangle. What can you say about the sum of the perpendicular distances from P to the sides of the triangle? Can you prove your conjecture?

A Little Light Thinking

Stage: 4 Challenge Level: Challenge Level:1

The problem Stars has a visual way of looking at relationships between numbers which might be useful in this problem.

The problem Shifting Times Tables offers an introductory challenge for exploring linear sequences.

You may prefer to experiment with this two-light version of the interactivity first.