A tangent of length 'L' is drawn from a point 'A' to a circle of radius 'r'. The length of tangent is  of r, then the shortest distance from point A to circle is (in units) A B C D

The question seems to be incomplete as it does not provide the ratio of the length of the tangent to the radius of the circle. However, I can provide a general solution.

The shortest distance from a point outside a circle to the circle is the perpendicular distance from the point to the center of the circle minus the radius of the circle.

If the length of the tangent (L) from point A to the circle is given as a multiple of the radius (r), say k (i.e., L = k*r), then we can use the Pythagorean theorem to find the distance from point A to the center of the circle (D).

Since the radius is perpendicular to the tangent at the point of tangency, we have a right triangle with the radius (r), the tangent (L), and the distance from point A to the center of the circle (D) as the sides. So, we have:

D^2 = r^2 + L^2 D^2 = r^2 + (kr)^2 D^2 = r^2 + k^2r^2 D^2 = r^2(1 + k^2) D = r*sqrt(1 + k^2)

So, the shortest distance from point A to the circle is D - r = r*sqrt(1 + k^2) - r.