Question

Find the area created by the overlapping circles given the following information.

Circle A: radius = 6in and m∠CAD = 90°
Circle B: radius = 8in and m∠CBD = 60°
Round your answer to the nearest hundredth if necessary.

5.83 in2
10.27 in2
16.10 in2
27.68 in2

Answer 1

16.10 in2

Explanation:

Find the area created by the overlapping circles given the following information.

Circle A: radius = 6in and m∠CAD = 90°

Circle B: radius = 8in and m∠CBD = 60°

Round your answer to the nearest hundredth if necessary.

5.83 in2

10.27 in2

16.10 in2

27.68 in2

Odyssey

Answer 2

The area of a circular sector of central angle α (in radians) in a circle of radius r is given by

... A = (1/2)r²×(α - sin(α))

Your area is expected to be computed as the sum of the areas of a sector with angle π/3 in a circle of radius 8 and a sector with angle π/2 in a circle of radius 6.

... A = (1/2)8²×(π/3 - sin(π/3)) + (1/2)6²×(π/2 - sin(π/2))

... A ≈ 16.07

Radii are in inches so the units of area will be in². The appropriate choice is

... 16.10 in²

_____

It should be noted that the geometry described is impossible. Chord CD of circle A will have length 6√2 ≈ 8.4853 inches. Chord CD of circle B will have length 8 inches. They cannot both be the same chord.