CRITICAL THINKING Find the area between the three congruent tangent circles. The radius of each circle is 6 inches. Round your answer to the nearest hundredth. Three congruent circles touch each other. The centers are marked as points A, B, and C. Equilateral triangle A B C is formed and the region inside triangle, but not in a circle, is shaded. The area is about a square inches.

Step-by-step explanation:

Given

--- The radius of each

Required

The area between them

See attachment for illustration of the question. (figure 1)

First, calculate the height of the equilateral triangle formed by the 3 radii (See figure 2)

Using Pythagoras theorem, we have:

Collect like terms

Take square roots

Expand

Split

Now, the area of the equilateral triangle can be calculated using:

Where

Next, is to calculate the area of the sector formed by 2 radii in each circle (figure 3).

Since the radii formed an equilateral triangle, then the central angle will be 60. So:

For the three circles, the area is:

Subtract the areas of the sectors (A2) from the area of the equilateral triangle (A1), to get the area between them.

Approximate

78.59 is the mean

step-by-step explanation:

step-by-step explanation: