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In the diagram, each of the three identical circles touch the other two. The circumference of each circle is 36. What is the perimeter of the shaded region?


 Jan 13, 2019

If we connect the centers of the circles, this will form an equilateral triangle


The two sides of this triangle meeting at any vertex will pass through the points of tangency where one circle meets the other two......these two tangent points form the endpoints of one side of the shaded region


Since the vertex angle of the triangle = 60°.....then the arc formed by one side of the shaded region = 1/6 the circumference of the circle = 6 units


So....the perimeter of the shaded region is 3 times this = 18  units



cool cool cool

 Jan 13, 2019

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