The circle circumscribing polygon is considered that if it applies to all of its vertices.
Remarkably, the center of this circle coincides with the intersection point of the perpendicular drawn from the midpoints of the sides of the polygon.
The radius of the circumscribed circle is entirely dependent on the polygon, around which it is described.
You will need
- Know the sides of the polygon, an area / perimeter.
Calculation of the radius of the triangle around circle.
? If the circle is described around a triangle with sides a, b, c, the area S and the angle, lying against the side of a, then its radius R can be calculated using the following formulas:
1) R = (a * b * c) / 4S-
2) R = a / 2sin ?.
Counting range circleCircumscribed around a regular polygon.
To calculate the radius circleCircumscribed about a regular polygon, you should use the following formula:
R = a / (2 x sin (360 / (2 x n))), where
a - side right mnogougolnika-
n - the number of its sides.