Let all the points on the curve $x^2+y^2-10 x=0$ are reflected about the line $y=x+3$. If the locus of the reflected points is in the form $x^2+y^2+g x+f y+c=0$, then the value of $(g+f+c)$ is

Let $x-y=0$ and $x+y=1$ be two perpendicular diameters of a circle of radius $R$. The circle will pass through the origin if $R$ is equal to

The number of common tangents to the circles $x^2+y^2-4 x-6 y-12=0, x^2+y^2+6 x+18 y+26=0$ is

Chords $$\mathrm{AB}$$ & $$\mathrm{CD}$$ of a circle intersect at right angle at the point $$\mathrm{P}$$. If the length of AP, PB, CP, PD are 2, 6, 3, 4 units respectively, then the radius of the circle is