? asked in Science & MathematicsMathematics · 10 years ago

trig area of a sector problem?

Three circles with radii of 4m, 2m, and 1m are externally tangent to each other. Find the area of the curved region between the circles.

1 Answer

  • L. G
    Lv 4
    10 years ago
    Favorite Answer


    Form a triangle ABC connecting the centers of the three circles. A is the center of the 4m radius, C is the center of the 2m radius and B is the center of the 1m radius.AC =6, AB= 5, and BC=3. The area of this triangle by Heron's formula is 7.48. By the Law of Cosines we get angles A,B, and C to be29.93d, 93.82d, and 56.25d.

    We subtract the areas of the three pie shaped sectors from the area of the triangle to get the answer.The area in the A circle is 16pi x(29.93/360) = 4.18

    B is .82 and C is 1.96

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