If a line drawn from a fixed point M a ,   b cuts the circle x 2 + y 2 = k 2 at C and D , then M C…

Let the line have slope $\tan \theta$

$\frac{x-a}{\cos \theta }=\frac{y-b}{\sin {\displaystyle \theta }}=r$

$x=a+r\cos \theta , y=b+r\sin \theta$

$\Rightarrow x^2+y^2=k^2$

$\Rightarrow {\left(a+r\cos \theta \right)}^2+(b+r\sin \theta {)}^2=k^2$

$r^2+2r(a\cos \theta +b\sin \theta )+a^2+b^2-k^2=0$

It has two roots $r_1=MC$ and $r_2=MD$

$r_1·r_2=a^2+b^2-k^2$

$MC\times MD=a^2+b^2-k^2$