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Inner-radius of a (convex) polygon

  1. Feb 11, 2009 #1
    Hi all,
    I want to know whether it is correct that every convex polygon has an inner-circle (& hence an inner-radius). I think it is only possible for triangle and for regular polygon. Am I right?

    If there is any convex N-gon having sides a_1,a_2,...,a_N which has an incircle, then what is the formula for the inner-radius in terms of the sides?


    Regards,
    NaturePaper
     
  2. jcsd
  3. Feb 11, 2009 #2
    If you draw a circle inside the convex polygon, it is not necessary that the circle will touch all the sides.
     
  4. Feb 12, 2009 #3
    then..??
     
  5. Feb 12, 2009 #4
    So Radius and center of the circle will differ with respect to the side you wish to touch with the circle. then what is the use of finding radius?
     
  6. Feb 13, 2009 #5
    @KnowPhysics,
    I think I'm missing something.

    It is well known that for a triangle with sides a_1, a_2, a_3 there is a (unique) circle inscribed
    in the triangle whose radius R is given by some formula involving the sides a_i's.

    My question was what about the general situation, i,e for any convex N-gon what will be the situation?

    Regards,
    NaturePaper
     
  7. Feb 13, 2009 #6
    i explained already, it is not necessary that the circle will touch all the sides. So Radius and center of the circle will differ with respect to the side you wish to touch with the circle.
     
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