Find the length of the chord formed by ${\mathrm{x}}^2+{\mathrm{y}}^2={\mathrm{a}}^2\text{ on the line }\mathrm{xcos}\mathrm{\alpha }+\mathrm{ysin}\mathrm{\alpha }=\mathrm{p}$

Equation of the circle is ${\mathrm{x}}^2+{\mathrm{y}}^2={\mathrm{a}}^2$
centre c(0,0), r = a
equation of the line is $\mathrm{xcos}\mathrm{\alpha }+\mathrm{ysin}\mathrm{\alpha }=\mathrm{p}$
$\mathrm{xcos}\mathrm{\alpha }+\mathrm{ysin}\mathrm{\alpha }-\mathrm{p}=0$
p = distance from the centre
$=\frac{|0+0-\mathrm{p}|}{\sqrt{{\cos }^2\mathrm{\alpha }+{\sin }^2\mathrm{\alpha }}}=\mathrm{p}$
$\text{ length of the chord }=2\sqrt{{\mathrm{a}}^2-{\mathrm{p}}^2}$