An Equilateral Triangle Of Side 20cm Is Inscribed In A Circle.Calculate The Distance Of A Side Of The Triangle From the Centre Of The Circle.
The medians of the triangle all pass through the center of the circle.
The medians intersect 2/3 of the way to the opposite side.
The altitude of the triangle is also one of the medians, and it has length 10√3.
So, r = (2/3)10√3 = 20/√3
For an equilateral triangle of side s, the circumradius is s/√3.
MATH
To calculate the distance of a side of an equilateral triangle from the center of the circle, we can use the properties of an equilateral triangle and the properties of a circle.
In an equilateral triangle, all sides and angles are equal. The radius of the circle is the distance from the center to any point on the circle. Let's consider one side of the equilateral triangle as the base.
Since the triangle is equilateral, the height of the triangle will be the distance from the top vertex to the midpoint of the base. This altitude will cut the base at a right angle, bisecting the base and forming two congruent right triangles.
Now, let's calculate the height of the equilateral triangle. In an equilateral triangle, the height is found by multiplying the length of one side by the square root of 3 divided by 2. Therefore, the height of the equilateral triangle is:
height = (side length) * √3 / 2
= 20 cm * √3 / 2
= 10√3 cm
Since the altitude bisects the base, the length from the center of the circle to one of the vertices of the triangle is equal to half the height. Therefore, the distance from the center of the circle to one side of the triangle is:
distance = 1/2 * height
= 1/2 * 10√3 cm
= 5√3 cm
Hence, the distance of a side of the equilateral triangle from the center of the circle is 5√3 cm.