Given a n-sided polygon with side length a. The task is to find the area of the cicumcircle of the polygon.
Input: n = 10, a = 3 Output: 1.99737 Input: n = 5, a = 6 Output: 3.02487
Approach: A regular n-gon divides the circle into n pieces, so the central angle of the triangle is a full circle divided by n: 360 deg/n.
Applying the law of cosines for the three side lengths of the triangle, we get
c2 = a2 + b2 – 2ab cos C
or, a2 = r2 + r2 – 2rr cos (360/n)
or, a2 = 2r2 – 2r2 cos (360/n)
or, c2 = r2 (2 – 2 cos (360/n))
Below is the implementation of the above approach:
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- Program to calculate area of Circumcircle of an Equilateral Triangle
- Find the centroid of a non-self-intersecting closed Polygon
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