Chord dividing circle , function Two chords $PA$ and $PB$ divide circle into three parts. The angle $PAB$ is a root of $f(x)=0$.
Find $f(x)$.
Clearly , $PA$ and $PB$ divides circle into three parts means it divides it into $3$ parts of equal areas
How can i find $f(x)$ then ?
thanks

Hint:  If you look up circular segment in Wikipedia, you should be able to write the area of the two segments cut off as a function of the angle between the chord and the tangent.  That angle is $\theta/2$ using the figure in the article.  Then the area of the circle that is left is what you want.  The question is whether you can write this area as a function of the angle between the chords (one variable) instead of the angles between the chords and their respective tangents (two variables).
