SOLUTION: An equilateral triangle, each side of which is 30cm, is inscribed in a circle. Find [a] the distance from the center of the circle to each side. [b] the radius of the circle.

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Question 1067832: An equilateral triangle, each side of which is 30cm, is
inscribed in a circle. Find [a] the distance from the
center of the circle to each side. [b] the radius of the
circle.
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
An equilateral triangle, each side of which is 30cm, is
inscribed in a circle. Find [a] the distance from the
center of the circle to each side. [b] the radius of the
circle.



We want to find d and r.

I could use trigonometry, but maybe you haven't had that,
so I'll only use the Pythagorean theorem and algebra:

For right triangle MNP, 

MN2 + NP2 = MP2

And for right triangle MNO,

MN2 + NO2 = MO2

Translating those in terms of d and r:













Substituting  for r+d in the second
equation of the system:







So we have the system:



Adding the two equations we get


 cm

Subtracting the two equations, we get


 cm

Edwin
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