1. ## Radius of Circle #2

Each of two tangents from an external point to a circle is 3cm long. The smaller arc which they intercept is 112degrees 30' 26''. Find the radius of the circle.

Help please, I really have no idea. Can you show it with illustrations, thanks!

2. Hello, reiward!

Each of two tangents from an external point to a circle is 3 cm long.
The smaller arc which they intercept is 112° 30' 26''.
Find the radius of the circle.
Code:
              * * *
*           *   A
*               o
*          r   *  * *    3
*         *
*           * θ     *      *
*       C o - - - - * - - - - o P
*           *       *      *
*         *
*          r   *  * *    3
*               o
*           *   B
* * *

The center of the circle is $\displaystyle C$; its radius is $\displaystyle r.$

Tangents $\displaystyle PA = PB = 3$
$\displaystyle \angle ACB \,=\,112^o30'13'' \quad\Rightarrow\quad \theta \:=\:\angle ACP \:\approx\:56.2536^o$

In right triangle $\displaystyle CAP\!:\;\;\sin\theta \:=\:\frac{3}{r} \quad\Rightarrow\quad r \:=\:\frac{3}{\sin\theta}$

ThereforeL .$\displaystyle r \:=\:\frac{3}{\sin56.2536^o} \;\approx\;3.6\text{ cm}$