Draw a circle of radius 3.3 cm. Draw a chord PQ of length 6.6 cm. Draw tangents to the circle at points P and Q. Write your observation about the tangents.

Answer: Chord PQ is a diameter (6.6 = 2 × 3.3), so the tangents at P and Q are parallel to each other.

Steps of construction:

1. Draw a circle with centre O and radius 3.3 cm.
2. Take point P on the circle. With centre P and radius 6.6 cm cut the circle at Q. Draw chord PQ; it passes through O because its length equals the diameter.
3. Draw line \(l\) through P perpendicular to OP, and line \(m\) through Q perpendicular to OQ.

Observation: both tangents are perpendicular to the same line PQ, so line \(l \parallel\) line \(m\). Tangents at the ends of a diameter are parallel.