A sector of a circle of radius 10 and central angle 60 degrees has a circle inscribed in it.  Find the diameter of the circle.


 May 13, 2020

The diameter of this smaller circle is  20/3  for this reason.


Take out any round coin. 

Trace around it on a sheet of paper and find the center of this circle.

You can then trace another six coins (of the same size) around the original coin so you have six outer circles

which are the same size an the innter circle.

Now, draw a circle whose center is the center of the original coin and is externally tangent to the six outer coins.

Draw radii of this larger circle which are tangent to each of the six ourter circles.

If you look at the center of the original circle and one of the outer circles, you have the picture to this problem.


From the center of the original circle to the edge of an outer circle is one adn one-half diameters.

Therefore, the diameter of each of the coins is two-thirds of 10.

 May 14, 2020

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