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?

Lightning Jan 13, 2019

#1**+1 **

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

CPhill Jan 13, 2019