An equilateral triangle of side 20cm is inscribed in a circle. Calculate the distance of the side of the triangles from the centre of the circle
In an equilateral triangle, the center of the circle coincides with the centroid of the triangle. The centroid divides each median in the ratio 2:1, meaning that the distance from the centroid to the midpoint of a side is 1/3 of the length of the median.
The median of an equilateral triangle is also the perpendicular bisector of the side it intersects. Therefore, the distance from the center of the circle to a side of the triangle is equal to 1/3 of the length between the center and the midpoint of the side.
The length of the median is 20 cm, so the distance from the center of the circle to a side of the triangle is (1/3) * (20 cm / 2) = 1/3 * 10 cm = 10/3 cm = 3.33 cm.
Therefore, the distance of the side of the triangle from the center of the circle is 3.33 cm.