Locus of the midpoints of the chords of contact of $x^2+y^2=2$ from the point on the line $3x+4y=10$ is a circle with centre P. If O be the origin then OP is equal to

Equation of the chord with midpoint (h, k) is

$\mathrm{hx}+\mathrm{ky}={\mathrm{h}}^2+{\mathrm{k}}^2\dots \left(1\right)$

chord of contact of $\left({\mathrm{x}}_1{\mathrm{y}}_1\right)\text{ is }{\mathrm{xx}}_1+{\mathrm{yy}}_1-2=0$  ….(2)

comparing, (1) & (2)
$$\begin{gathered} {\mathrm{x}}_1=\frac{2 \mathrm{h}}{{ \mathrm{h}}^2+{\mathrm{k}}^2}\text{ and }{\mathrm{y}}_1=\frac{2\mathrm{k}}{{\mathrm{h}}^2+{\mathrm{k}}^2} \\ \left({\mathrm{x}}_1,{\mathrm{y}}_1\right)lies\text{ on }3\mathrm{x}+4\mathrm{y}=10\Rightarrow 6 \mathrm{h}+8\mathrm{k}=10\left({ \mathrm{h}}^2+{\mathrm{k}}^2\right) \\ \therefore \text{ Locus of }(\mathrm{h},\mathrm{k})\text{ is }{\mathrm{x}}^2+{\mathrm{y}}^2-\frac{3}{5}\mathrm{x}-\frac{4}{5}\mathrm{y}=0 \\ \text{ which is circle with centre }\mathrm{P}\left(\frac{3}{10},\frac{4}{10}\right) \\ \therefore \mathrm{OP}=\frac{1}{2} \end{gathered}$$