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A circle is circumscribed about an equilateral triange with side a. What is the diameter of the circle?
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Thank you for understanding, and happy exploring!
In a equilateral tiangle, the distance from 1 vertex to the center of graivty is equal to 2/3 the height : h. This distance is also the radius of the circle from which we are looking for the diameter.
At the same time, we have:
a^2=h^2 + a^2/4
<=> h = sqrt(3)/2*a
Thus,
The radius = 2/3 * sqrt(3)/2*a = sqrt(3)/3 * a
and
The diameter = 2*sqrt(3)/3 * a
At the same time, we have:
a^2=h^2 + a^2/4
<=> h = sqrt(3)/2*a
Thus,
The radius = 2/3 * sqrt(3)/2*a = sqrt(3)/3 * a
and
The diameter = 2*sqrt(3)/3 * a
