Question

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.

Answer 1

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

Answer 2

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=400-100 , /OM/=√300 /OM/=17.33

Answer 3

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 right-angled 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.

Answer 4

tacs vry mch

Answer 5

The radius is 20cm ÷ 2 =10, equilateral triangle = 60° degree and 60° bisected to 2 = 30° ;tan 30° = × ÷ 10,0.5774 = × ÷ 10, 0.5774 x 10 = ×, × =5.774 or × = 5.77cm