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 cicle
the center of the triangle (and the circle) is 1/3 the distance from a base (side) to a vertex along an altitude
I need the answer
To calculate the distance of a side of an equilateral triangle from the center of the circle, we can use some basic properties of the equilateral triangle and circle.
1. Draw the equilateral triangle inscribed in the circle:
- The length of each side of the triangle is given as 20 cm.
- Connect the center of the circle to each vertex of the triangle.
- You'll notice that you have three radii (lines from the center of the circle to the vertices of the triangle), bisecting the angles of the triangle.
2. Determine the radius of the circle:
- Since the triangle is equilateral, each internal angle is 60 degrees.
- Draw a perpendicular line from the center of the circle to one side of the triangle, dividing it into two equal line segments.
- You now have a right triangle with one side being the radius of the circle (r), the hypotenuse being the side of the equilateral triangle (20 cm), and the angle opposite the radius being 30 degrees (half of the internal angle).
- You can use trigonometry to calculate the radius (r) using the formula: r = (side length of the triangle) / (2 * cos(angle)).
- r = 20 cm / (2 * cos(30 degrees)).
3. Calculate the distance of a side of the triangle from the center:
- Since the distance from the center to a side of the triangle is equal to the radius of the circle, you can use the previously calculated radius as the answer.
- Substitute the radius value (r) into the formula: distance = r.
So, the distance of a side of the equilateral triangle from the center of the circle is the radius of the circle, which can be calculated as r = 20 cm / (2 * cos(30 degrees)).