To end a week of geometry problems, it is no surprise that PMQ7 is also a geometric puzzle.

The diagram shows five circles, each with integer radius, all touching the base of the large triangle. The four smaller circles all touch their two neighbouring circles, with the large circle touching all four. The two sides of the triangle each touch two of the circles.

Let the radii of the circles be

*a*,

*b*and

*c*, such that

*a*>

*b*>

*c*.

Given that

*c*has a length of 4 units, find the area of the large triangle. You may leave it as an exact solution.

As always, I would like to see a method. As an interim solution, find the radii of all three circles.

Good luck!

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**This PMQ7 competition closes on Sunday 24 February at 23:59 GMT**.

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