1. ## 2003 Circles

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