In a circle with radius R, the shortest distance between two parallel tangents is equalto∶(a) R(b) 2R(c) 2πR(d) πR

The shortest distance between two parallel tangents in a circle with radius R is 2R. So, the correct answer is (b) 2R.

Here's the step by step explanation:

1. Draw a circle with radius R.
2. Draw two parallel tangents to the circle.
3. Draw two radii from the center of the circle to the points where the tangents touch the circle.
4. These two radii are perpendicular to the tangents (as radius at the point of contact is perpendicular to the tangent).
5. Now, you have two right-angled triangles, each with one side as the radius of the circle (R) and the hypotenuse from the center of the circle to a point on the tangent.
6. The distance between the two parallel tangents is the other side of these right-angled triangles, which is also the difference in length between the two hypotenuses.
7. Since the two triangles are identical, this distance is equal to 2R.