Tangents are perpendicular

$$\begin{gathered} \mathrm{Locus} \mathrm{of} \mathrm{point} \mathrm{of} \mathrm{intersection} \mathrm{perpendicular} \mathrm{tangents} \mathrm{drawn} \mathrm{to} \\ \mathrm{each} \mathrm{of} \mathrm{the} \mathrm{circles} {\mathrm{x}}^2+{\mathrm{y}}^2={\mathrm{a}}^2 \mathrm{and} {\mathrm{x}}^2+{\mathrm{y}}^2={\mathrm{b}}^2 \mathrm{is} {\mathrm{x}}^2+{\mathrm{y}}^2={\mathrm{a}}^2 +{\mathrm{b}}^2 \\ \mathrm{So},\mathrm{required} \mathrm{tangent} \mathrm{is} {\mathrm{x}}^2+{\mathrm{y}}^2=20 \end{gathered}$$