The straight line x + 2y = 1 meets the coordinate axes at A and B. A circle is drawn through A, B and the origin. Then the sum of perpendicular distances from A and B on the tangent to the circle at the origin is :

If the area of an equilateral triangle inscribed in the circle x² + y² + 10x + 12y + c = 0 is $$27\sqrt 3 $$ sq units then c is equal to :

If a circle C passing through the point (4, 0) touches the circle x² + y² + 4x – 6y = 12 externally at the point (1, – 1), then the radius of C is :

If the circles

x² + y² $$-$$ 16x $$-$$ 20y + 164 = r²  

and  (x $$-$$ 4)² + (y $$-$$ 7)² = 36

intersect at two distinct points, then :