The locus of midpoints of the chord of the circle $x^2+y^2=25$ which pass through a fixed point (4, 6) is a circle. The radius of that circle is 
 

Let P $({\mathrm{x}}_1, {\mathrm{y}}_1)$ mid-point of chord 

 equation of chord is ${\mathrm{S}}_1={\mathrm{S}}_{11}$

 $$\begin{gathered} {\mathrm{xx}}_1+{\mathrm{yy}}_1-25={{\mathrm{x}}_1}^2+{{\mathrm{y}}_1}^2-25 \\ {{\mathrm{x}}_1}^2+{{\mathrm{y}}_1}^2-{\mathrm{xx}}_1-{\mathrm{yy}}_1=0 \end{gathered}$$

it is passing through (4, 6)  then locus of P is 

$$\begin{gathered} {\mathrm{x}}^2+{\mathrm{y}}^2-4\mathrm{x}-6\mathrm{y}=0 \\ \mathrm{r}=\sqrt{4+9}=\sqrt{13} \end{gathered}$$