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# Circles on a Triangle

On this diagram, the circles centred at A and C touch.

Find the length CE.

*This problem is taken from the World Mathematics Championships*## You may also like

### Some(?) of the Parts

### Triangle Midpoints

### Fermat's Poser

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- Problem
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On this diagram, the circles centred at A and C touch.

Find the length CE.

You can find more short problems, arranged by curriculum topic, in our short problems collection.

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

You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?

Find the point whose sum of distances from the vertices (corners) of a given triangle is a minimum.