2 5cm radius circles inscribed inside a 15cm circle

In summary, the problem involves two identical circles with a radius of 5cm touching each other externally and both touching an arc length of a larger 15cm circle. We are asked to find the perimeter and area of the region between the smaller circles and the arc length of the larger circle. Using the equation s=r times angle, we can calculate the perimeter to be 35π/3 and the area to be 25/6(5π-6√3). The solution assumes that the smaller circles lie inside the larger circle.
  • #1
KKW
3
0

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

 
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  • #2
KKW said:
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! :smile:

Hint: the line from the centre of the big circle to the two tangent points goes through the centres of the small circles. :wink:
 
  • #3
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.

[tex]A=\frac{25}{6}(5\pi-6\sqrt{3})[/tex]

[tex]P=\frac{35\pi}{3}[/tex]

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.
 
Last edited:

Related to 2 5cm radius circles inscribed inside a 15cm circle

What is the diameter of each inscribed circle?

The diameter of each inscribed circle is 10cm, which is equal to twice the radius of the inscribed circle.

How many circles can fit inside the larger circle?

There are two circles that can fit inside the larger circle, as given by the problem.

What is the area of each inscribed circle?

The area of each inscribed circle is approximately 78.54 square cm, which is calculated using the formula πr2.

What is the total area of all three circles combined?

The total area of all three circles combined is approximately 235.62 square cm, which is the sum of the areas of the two inscribed circles and the larger circle.

What is the distance between the centers of each inscribed circle?

The distance between the centers of each inscribed circle is equal to the radius of the larger circle, which is 7.5cm. This can be calculated using the Pythagorean theorem.

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