Three circles with radius r are drawn as shown, each with its center on the circumference of the other two circles. A, B and C are the centers of the three circles. Prove that an expression for the area of the shaded region is:

Three circles with radius r are drawn as shown, each with its center on the circumference of the other two circles. A, B and C are the centers of the three circles. Prove that an expression for the area of the shaded region is:

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter8: Areas Of Polygons And Circles

Section8.5: More Area Relationships In The Circle

Problem 10E: Suppose a circle of radius r is inscribed in a rhombus, each of whose sides has length s. Find an...

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Question

3)
Three circles with radius r are drawn as shown, each with its center on the circumference of the other two
circles. A, B and C are the centers of the three circles. Prove that an expression for the area of the shaded
region is:

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