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Math Help - 2003 Circles

  1. #1
    Newbie darknight's Avatar
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    2003 Circles

    C is a circle with radius r. C1, C2, C3.....C2003 are unit(i.e of length 1 unit) circles placed along the circumference of C touching C externally. Also the pairs (C1,C2); (C2,C3); (C2002,C2003); (C2003,C1) touch each other.
    Then r is equal to:

    a) cosec (pi/2003)
    b) sec (pi/2003)
    c) [cosec(pi/2003)] - 1
    d) [sec(pi/2003)] - 1
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  2. #2
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    Quote Originally Posted by darknight View Post
    C is a circle with radius r. C1, C2, C3.....C2003 are unit(i.e of length 1 unit) circles placed along the circumference of C touching C externally. Also the pairs (C1,C2); (C2,C3); (C2002,C2003); (C2003,C1) touch each other.
    Then r is equal to:

    a) cosec (pi/2003)
    b) sec (pi/2003)
    c) [cosec(pi/2003)] - 1
    d) [sec(pi/2003)] - 1
    1. Draw a sketch.

    2. You are dealing with a 2003-gon. The radius of the circumscribing circle is r +1 and the perimeter of the 2003-gon is 4006.

    3. Use isosceles triangles to calculate the central angle.
    Attached Thumbnails Attached Thumbnails 2003 Circles-krsaufkrs.png  
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