Solution

To draw a circle of radius 2.7 cm and a tangent to the circle at any point on it, follow these steps:

1. Draw a point O as the center of the circle.

2. Draw a circle with center O and radius 2.7 cm.

3. Choose any point P on the circumference of the circle.

4. Draw a line segment OP to connect point O with point P.

5. Draw a line perpendicular to line segment OP at point P. To do this, use a compass to draw an arc centered at P that intersects the circle at points X and Y. Then draw a line through point P that is perpendicular to line segment XY.

6. The line segment drawn in step 5 is the required tangent to the circle at point P.

Note that the tangent is unique, and it is perpendicular to the radius of the circle that passes through point P.