SOLUTION: If an equilateral triangle is circumscribed about a circle of radius 10 cm, determine the side of the triangle.

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Question 782788: If an equilateral triangle is circumscribed about a circle of radius 10 cm, determine the side of the triangle.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Side AC is tangent to the circle, perpendicular to radius OD at the point of tangency (point D).
We can draw 6 angles congruent with AOD connecting the center with points of tangency and vertices, and their measures add to 360%5Eo,
so AOD measures 360%5Eo%2F6=60%5Eo
Using trigonometry, we know that
DA%2FOD=tan%2860%5Eo%29 --> DA%2F10cm=sqrt%283%29 --> DA=%2810cm%29%2Asqrt%283%29
and since CD+=+DA,
CA+=+CD%2BDA=+2DA+=2%2A%2810cm%29%2Asqrt%283%29=20%2Asqrt%283%29cm
Rounding, we get an approximmate value of highlight%2834.64cm%29.