Thread: 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).

The problem above complete radian answer(not in function of any variables)

I could set the answer in funcion of the central angle= , and is:


Any suggest would be appretiated.

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.

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.

Thank you for the answer.