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.
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.
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
tacs vry mch
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
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
To calculate the distances of a side of the equilateral triangle from the center of the circle, we can use the properties of an equilateral triangle and the circle.
First, let's draw the triangle and label the important points.
In an equilateral triangle, all three sides are congruent, meaning they have the same length. In this case, each side of the triangle has a length of 20 cm.
The center of the circle is also the center of the equilateral triangle and is represented by point O. The distance between the center of the circle and any vertex of the equilateral triangle is called the radius of the circle and is denoted by r.
To determine the distances of a side of the triangle from the center of the circle, we need to find the radius of the circle first.
In an equilateral triangle, the radius of the circumcircle (a circle passing through all three vertices) can be calculated using the formula:
r = (s * √3) / 3
Where s is the length of a side of the triangle.
Substituting s = 20 cm into the formula:
r = (20 * √3) / 3
Now we can calculate the distance of a side of the triangle from the center of the circle.
In an equilateral triangle, the distance of a side from the center is equal to 2/3 times the height of the triangle.
The height of an equilateral triangle can be found using the formula:
h = (s * √3) / 2
Substituting s = 20 cm into the formula:
h = (20 * √3) / 2
Finally, we can calculate the distance by multiplying the height by 2/3:
Distance = (2/3) * h
Distance = (2/3) * [(20 * √3) / 2]
Simplifying the expression:
Distance = (20 * √3) / 3
Therefore, the distances of a side of the triangle from the center of the circle is equal to (20 * √3) / 3, which is approximately 11.55 cm.