An equilateral triangle of side 20cm is inscribed in a circle. Calculate the distance of a side of the triangle from the center of the circle
If you draw the diagram, it should be clear that the distance from the center of the circle to a side of the triangle is 10/√3
Lots of 30-60-90 triangles
2+2
To calculate the distance of a side of the equilateral triangle from the center of the circle, we need to find the radius of the circle.
In an equilateral triangle, all sides are equal in length. Since the side length of the triangle is given as 20 cm, each side is 20 cm long.
Now, let's consider one side of the equilateral triangle as the base. When we draw the altitude (perpendicular) from the center of the circle to this side, it will divide the side into two equal halves, forming a right triangle.
Since the triangle is equilateral, the altitude will bisect the base and form two congruent 30-60-90 right triangles.
In a 30-60-90 triangle, the length of the hypotenuse (the side opposite the right angle) is twice the length of the shorter leg. The length of the longer leg is √3 times the length of the shorter leg.
So, in our equilateral triangle, if the side length is 20 cm, the length of the shorter leg of the right triangle formed by the altitude is half of the side length, which is 20/2 = 10 cm.
Using the properties of a 30-60-90 triangle, the longer leg (the distance from the center of the circle to the side of the equilateral triangle) would be √3 times the shorter leg.
Therefore, the distance from the center of the circle to a side of the equilateral triangle is √3 times the length of the shorter leg, which is √3 * 10 cm = 10√3 cm.
Hence, the distance of a side of the equilateral triangle from the center of the circle is 10√3 cm.