get length of line connecting sector of a circle What is the formula for getting the length of a line (in this case the red one) connecting starting point and end point of an arc, given the circle's radius $R$ and $\angle A$?


The triangle obtained by joining the end-points of the chord (red line) to the center of circle, we get an isosceles triangle.
Thus, dropping perpendicular to the chord, we get right triangle in which we have   $$\sin\frac{A}{2}=\frac{\left(\frac{\text{length of chord}}{2}\right)}{\text{radius}}=\frac{\left(\text{length of chord}\right)}{2R}$$ $$\implies \color{blue}{\text{length of chord}=2R\sin \frac{A}{2}}$$  
