Question

Find the co-ordinates of the point of intersection of the tangents drawn to the circle $x^2+y^2=a^2$ at the points whose parametric angles are $\alpha$ and $\beta$.

Answer 1

Solve $x\cos \alpha +y\sin \alpha -a=0$
and $x\cos \beta +y\sin \beta -a=0$
by the method of cross-multiplication.
$(\frac{a\cos \frac{\alpha +\beta }{2}}{\cos \frac{\alpha -\beta }{2}},\frac{a\sin \frac{\alpha +\beta }{2}}{\cos \frac{\alpha -\beta }{2}})$.