2 5cm radius circles inscribed inside a 15cm circle

[KKW]

Homework Statement

2 identical circles of radius 5cm touching each other externally and both are touching an arc length of a larger 15cm circle. Find the 1. perimeter and 2. area of the region between the 2 smaller circles and the arc length of the larger circle

Homework Equations

s=r times angle

The Attempt at a Solution

 

[tiny-tim]

2 identical circles of radius 5cm touching each other externally and both are touching an arc length of a larger 15cm circle. Find the 1. perimeter and 2. area of the region between the 2 smaller circles and the arc length of the larger circle

Hi KKW!

Hint: the line from the centre of the big circle to the two tangent points goes through the centres of the small circles.

 

[ben297]

I really like this problem. I won't give away how I solved it but I'd be interested to know if others get the same answers.

$$A=\frac{25}{6}(5\pi-6\sqrt{3})$$

$$P=\frac{35\pi}{3}$$

Note: The problem doesn't explicitly state if the two smaller circles lie inside or outside the larger circle. The values given above assume the former.