Length of the chord joining the points $P(\alpha)$ and $Q(\beta)$ on the circle $x^{2}+y^{2}=a^{2}$ is
- $2a \cos \left(\dfrac{\alpha-\beta}{2}\right)$
- $2a \sin \left(\dfrac{\alpha-\beta}{2}\right)$
- $2a \tan \left(\dfrac{\alpha-\beta}{2}\right)$
- $2a \csc \left(\dfrac{\alpha-\beta}{2}\right)$
The distance between two points on a circle with polar angles alpha and beta is given by the chord length formula 2a * sin((alpha - beta) / 2).
Using the distance formula, the length of the chord joining the points P(a cos A, a sin A) and Q(a cos B, a sin B) on the circle x squared plus y squared equals a squared is calculated as the square root of the sum of the squared differences of the coordinates. Applying the trigonometric identities for the sine and cosine of half angles, this distance simplifies to 2a multiplied by the absolute value of the sine of half the difference of the angles. Therefore, the length of the chord is 2a sin((alpha minus beta)/2).