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Some(?) of the Parts

A circle touches the lines OA, OB and AB where OA and OB are perpendicular. Show that the diameter of the circle is equal to the perimeter of the triangle

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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?

Rotating Triangle

Stage: 3 and 4 Challenge Level: Challenge Level:1

Two smaller circles, centres $B$ and $C$ touch each other externally and touch the circle centre $A$ internally.

What happens to the perimeter of triangle $ABC$ as the two smaller circles roll around touching the inside rim of the bigger circle or as the two smaller circles vary in size?

Move the sliders to change the radii of the smaller circles and drag the point $B$ to move the circles.


Created with GeoGebra


You might like to download your own free copy of GeoGebra from the link above and draw this dynamic diagram for yourself. You will find it easy to get started on GeoGebra with the Quickstart guide for beginners.