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

If two circles which pass through the points $$(0, a)$$ and $$(0,-a)$$ and touch the line $$\mathrm{y}=\mathrm{m} x+\mathrm{c}$$, cut orthogonally then