If the circles

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

and  (x $$-$$ 4)² + (y $$-$$ 7)² = 36

intersect at two distinct points, then :

Three circles of radii a, b, c (a < b < c) touch each other externally. If they have x-axis as a common tangent, then :

If a circle C, whose radius is 3, touches externally the circle,
$${x^2} + {y^2} + 2x - 4y - 4 = 0$$ at the point (2, 2), then the length of the intercept cut by this circle C, on the x-axis is equal to :

If the tangent at (1, 7) to the curve x² = y - 6

touches the circle x² + y² + 16x + 12y + c = 0, then the value of c is :