Government senior college ikoyi
posted by Monday Godwin .
An equilateral triangle of side 20cm is inscribed in a circle.calculate the distances of a side of the triangle from the centre of the circle.

Basically the inradius of the equilateral triangle. The formula for that is
inradius * semiperimeter (half the perimeter) = area
We know that the formula for calculating the area of a equilateral triangle is s^2 sqrt 3 /4 so we get 100sqrt3 as the area of the equilateral triangle.
Then, inradius * semiperimeter = 100sqrt 3
So, the semiperimeter is equal to half the perimeter. Therefore, 20+20+20 / 2 = 30.
The formula is now inradius * 30 = 100sqrt3
So, the inradius is 100sqrt3 / 30 =
10sqrt3/3 
the Angel is /ABC/ inscribed in a circle center O an M radius =20cm, /AM/=10cm /AO/=20cm than /OM/2=\AO/2 /AM/2 which equal to /OM/2=400100 , /OM/=√300 /OM/=17.33

An equilateral triangle has all the sides to be 60°. Divide the triangle into halves which will make the base to be 10cm and 10cm. Bisect angle 60° to the centre of the circle or triangle which will give you 30°. You then have a mini right angled triangle inside the large one. Since we are looking for the distance of a side of the triangle from the centre of the circle, we call it X which is 'opposite' of the mini rightangled triangle.
Now we have opposite to be X and adjacent to be 10 so we have to use tangent which is opposite over adjacent.
Tan 30°= X÷10
0.5774= X÷10
0.5774×10= X
X=5.774.
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