Its 12cm because when we draw the chord which touches point of contact to the circle of two parallel tangents it forms diameter the longest chord and diameter is double the radius

Introduction:
To find the distance between the point of contact of two parallel tangents to a given circle, we can make use of the concept of the chord of contact. The chord of contact is a line segment joining the points of contact of tangents drawn from an external point to a circle.

Given:
- Radius of the given circle = 6 cm

Approach:
1. Draw a circle with the given radius of 6 cm.
2. Draw a line passing through the center of the circle, which will be the line of symmetry for the tangents.
3. Mark two points on the line of symmetry, which will represent the point of contact of the tangents.
4. Draw two tangents from the marked points to the circle. These tangents will be parallel to each other.
5. The distance between the points of contact of these tangents can be found by using the property that the chord of contact is perpendicular to the line joining the center of the circle to the external point.
6. Draw a line perpendicular to the line of symmetry passing through the center of the circle. This line will intersect the line of symmetry at a right angle.
7. The distance between the points of contact of the tangents is equal to the length of this perpendicular line.

Calculation:
- The length of the perpendicular line can be found using the Pythagorean theorem.
- The perpendicular line forms a right-angled triangle with the line of symmetry and the radius of the circle.
- Let the length of the perpendicular line be 'x'.
- The length of the line of symmetry is equal to the diameter of the circle, which is twice the radius.
- Therefore, the length of the line of symmetry = 2 * 6 cm = 12 cm.
- The length of the radius of the circle = 6 cm.
- Using the Pythagorean theorem, we can write:
x^2 + 6^2 = 12^2
x^2 + 36 = 144
x^2 = 144 - 36
x^2 = 108
x = √108
x = 6√3 cm

Answer:
The distance between the point of contact of two parallel tangents to the given circle of radius 6 cm is 6√3 cm.