Answer to the Problem of the Week for the week of March 14, 2005 |
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Three Tangent Circles |
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In honor of PI DAY (3/14), you will need to use pi in your solution of this
week's problem. |
Solution to the Problem: The shaded area = 1.857 square inches.The following facts were used to solve this problem:
Then AB = 10 inches, BC = 6 inches, and AC = 8 inches. This forms a right triangle since 62 + 82 = 102. Therefore, angle C is the right angle. Observe that the shaded area (in red in the diagram above) is equal to the area of triangle ABC minus the areas of the three sectors (these are shown as tan, grey, and cyan in the diagram below). The area of triangle ABC = 1/2 * 6 * 8 = 24 square inches.
The measure of angle C has been determined to be 90°, The area of sector A = 36.8699/360 * pi * 6 2 = 11.583 square inches.
To determine angle B: B = Tan-1
(8/6) = 53.130°.
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1. Keith Mealy | Cincinnati, Ohio |
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3. Arsalan Heydarian | Harrisonburg, Virginia |
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