Question

If the chord of contact of the tangents drawn from $(\alpha ,\beta )$ to the circle $x^2+y^2=a^2$ subtends right angle at the centre then prove that ${\alpha }^2+{\beta }^2=2a^2$.

Answer 1

$\begin{array}{c}\Rightarrow AL=a\cos ec{45}^{\circ }=a\sqrt{2}\\ \Rightarrow x^2+y^2={\left(a\sqrt{2}\right)}^2\\ \Rightarrow x^2+y^2=2a^2\\ Satisfypoint\left(\alpha ,\beta \right)inequation\\ {\alpha }^2+{\beta }^2=2a^2\end{array}$