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

Answer: The line through M perpendicular to radius PM is the required tangent.

Analysis: A line perpendicular to a radius at its outer end is a tangent to the circle.

Steps of construction:

1. Draw a circle with centre P and radius 3.2 cm. Take any point M on it.
2. Draw ray PM and extend it beyond M.
3. Draw line \(l\) through M perpendicular to ray PM (with centre M cut equal arcs on the ray on both sides of M, then draw the perpendicular bisector of that segment).
4. Line \(l\) is the required tangent at M.