Posted by **Rox** on Wednesday, February 13, 2013 at 11:52am.

Three circles, each with a radius of 10, are mutually tangent to each other. The area enclosed by the three circles can be written as a√b−cπ, where a, b and c are positive integers, and b is not divisible by a square of a prime. What is the value of a+b+c?

- maths -
**Steve**, Wednesday, February 13, 2013 at 12:42pm
Draw lines joining the centers of the circles. That is an equilateral triangle with side 10.

Area of triangle is 1/2 * 5 * 5√3 = 25/2 √3

Now, the angles of the triangle are all π/3, so, since the area of a sector of a circle is a = 1/2 r^2 θ, each sector has area 1/2 * 25 * π/3 = 25/6 π

So, the area in between all the circles is the area of the triangle, less the total area of the 3 sectors.

I think you can take it from here.

- maths - correction -
**Steve**, Wednesday, February 13, 2013 at 12:43pm
Oops. I was thinking diameter of 10, not radius. Adjust calculations accordingly.

## Answer this Question

## Related Questions

- maths - Three circles, each with a radius of 10, are mutually tangent to each ...
- geometry!!!!!!!!!! - Three circles, each with a radius of 10, are mutually ...
- geometry - Three circles, each with a radius of 10, are mutually tangent to each...
- MATH - Three circles, each with a radius of 10, are mutually tangent to each ...
- matsh - The picture below shows a figure in the complex plane, consisting of two...
- PLEASE HELP TANGENTS AND CIRCLES PROBLEM GEOMETRY - PLEASE HELP I REALLY NEED ...
- geometry - Three circles are externally tangent to one another. The radius of ...
- maths - there are two circles touching each other at one point. The radius of ...
- Maths - Three circles are placed on a plane in such a way that each circle just ...
- Maths - Three circles are placed on a plane in such a way that each circle just ...