# Thread: circle incribed in a circular sector

1. ## circle incribed in a circular sector

Find out the central angle of the circle sector.
If the length of its arc is equal to the perimeter of
the circunference inscribed in it(circle sector).

I could set the answer in funcion of the central angle=$\displaystyle \theta$, and is:
$\displaystyle \theta (\csc\theta+1)=\pi$

Any suggest would be appretiated.

2. ## Re: circle incribed in a circular sector

Your equation is correct. Now look at the numerical solution and try to guess how it relates to pi. After guessing, verify that the number indeed satisfies the equation. It is clear from the graph that there are no solutions in the interval [0, pi], but this could be proved more precisely.

3. ## Re: circle incribed in a circular sector

Originally Posted by emakarov
Your equation is correct. Now look at the numerical solution and try to guess how it relates to pi. After guessing, verify that the number indeed satisfies the equation. It is clear from the graph that there are no solutions in the interval [0, pi], but this could be proved more precisely.