Circles
16.0 Equation of chord joining two points on circle
16.0 Equation of chord joining two points on circle
Equation of chord $PQ$ to circle ${x^2} + {y^2} = {a^2}$ joining points $P(\alpha )$ and $Q(\beta )$ on it is given by the 
equation $$x\cos \frac{{\alpha + \beta }}{2} + y\sin \frac{{\alpha + \beta }}{2} = a\cos \frac{{\alpha - \beta }}{2}$$
equation $$x\cos \frac{{\alpha + \beta }}{2} + y\sin \frac{{\alpha + \beta }}{2} = a\cos \frac{{\alpha - \beta }}{2}$$where $\alpha $ and $\beta $ are parameters of two points $P$ and $Q$ on circle.
