# Math Help - 2003 Circles

1. ## 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

2. Originally Posted by darknight
$C$ 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.