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How to find the radius

How to find the radius

If one can construct a polygon inscribed and circumscribed circles, that this area of ​​the polygon is less than the area of ​​the circumscribed circle, but most of the area of ​​the inscribed circle.

Some polygons are known formula to find the radius of the inscribed and circumscribed circles.



Inscribed in the polygon is called a circle tangent to all the sides of the polygon. For triangle formula radius incircle: r = ((p-a) (p-b) (p-c) / p) ^ 1/2, where p - poluperimetr- a, b, c - side of the triangle. For regular triangle simplified formula: r = a / (2 * 3 ^ 1/2), and - side of the triangle.


Circumscribing the polygon called suchcircle on which lie all polygon vertices. For triangle radius of the circle is given by: R = abc / (4 (p (p-a) (p-b) (p-c)) ^ 1/2), where p - poluperimetr- a, b, c - side of the triangle. formula is easier for the equilateral triangle: R = a / 3 ^ 1/2.


For polygons is not always possible to find outthe ratio of the radii of the inscribed and circumscribed circles and the length of its sides. Most are limited to the construction of circles around the polygon, and then the physical dimension radius circles using instrumentation or vector space.
To construct the circumscribed circle of a convexpolygon build bisector of its two corners, at their intersection is the center of the circumscribed circle. Radius is the distance from the intersection point of the bisectors to the top of every angle of the polygon. The center of the inscribed circle lies at the intersection of the perpendiculars built inside the polygon of the centers of the sides (these are called the median perpendiculars). Enough to build two such perpendicular. The radius of the inscribed circle is equal to the distance from the point of intersection of the median perpendicular to the sides of the polygon.

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