Asked in: July 2024 board paperConstruct 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.

Steps of construction:

1. Draw a circle with centre P and radius 3.2 cm.
2. Take any point M on the circle and draw ray PM.
3. Draw line l through M perpendicular to ray PM (using compass arcs on both sides of M on ray PM).
4. Line l is the required tangent at M.

[Figure: circle with centre P, radius 3.2 cm; radius PM; line l through M at right angles to PM.]

Reason: a line perpendicular to the radius at its point on the circle is a tangent (converse of the tangent theorem).