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Regular Polygon

A regular polygon is a polygon which has all its sides equal and all its angles equal.
  1. Each interior angle of a regular polygon of n sides is 70376.pngright angles = 70370.png radians.
  2. The circle passing through all the vertices of a regular polygon is called its circumscribed circle. If a is the length of each side of a regular polygon of n sides, then the radius R of the circumscribed circle is given by 70364.png.
  3. The circle which can be inscribed within the regular polygon so as to touch all its sides is called its inscribed circle.
     
    Again if a is the length of each side of a regular polygon of n sides, then the radius r of the inscribed circle is given by 70107.png
     
    74320.png
  4. The area of a regular polygon is given by Δ = n × area of triangle OAB
     
    70101.png, (in terms of side)
     
    70095.png, (in terms of inradius)
     
    70089.png, (in terms of circumradius)

Inequality

In ΔABC, cos A + cos B + cos C70083.png
 
Also cos A + cos B + cos C = 1 + 470077.png
 
70071.png
 
In ΔABC, r = 4R70065.png R ≤ 2r




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