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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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Show that for any triangle it is always possible to construct 3 touching circles with centres at the vertices. Is it possible to construct touching circles centred at the vertices of any polygon?


Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

If you're stuck why not try this proof sorting activity? Cut out the pieces and see if you can rearrange them into a coherent proof.

If you have Java enabled, you can experment with the interactive diagram below by clicking and dragging the red points