Construct a tangent to a circle with centre P and radius 3.2 cm at any point M on it

Here are the steps to construct a tangent to a circle with centre P and radius 3.2 cm at any point M on it:

1. Draw a circle with centre P and radius 3.2 cm using a compass.

2. Choose a point M on the circumference of the circle.

3. Draw a line segment PM from the centre of the circle to the point M.

4. Using a compass, with M as the centre and the same radius (PM), draw a circle. This will intersect the line PM at a new point, let's call it N.

5. Draw a line from M through N. This line is perpendicular to PM and will be the tangent to the circle at point M.

6. You can verify this by measuring the angle between PM and the tangent line. It should be 90 degrees.

Remember, a tangent to a circle is a line that touches the circle at exactly one point. The line you have drawn from M through N is touching the circle at M and nowhere else, so it is a tangent.