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

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

Rough figure: a circle with centre O; diameter PQ through O; a line through P and a line through Q, each perpendicular to PQ.

Steps of construction:

1. Draw a circle with centre O and radius 3.3 cm.
2. Take a point P on the circle. With P as centre and radius 6.6 cm, draw an arc cutting the circle at Q. Draw chord PQ; since \(6.6 = 2 \times 3.3\), PQ passes through O and is a diameter.
3. Produce seg PQ on both sides.
4. At P draw line \(l \perp\) PQ, and at Q draw line \(m \perp\) PQ (using arcs and bisecting). Lines \(l\) and \(m\) are the required tangents.

Final figure (as drawn): circle with centre O (radius 3.3 cm); diameter PQ = 6.6 cm through O; line PQ produced on both sides; the tangent lines \(l\) at P and \(m\) at Q with right-angle marks and construction arcs.

Observation: chord PQ of length 6.6 cm is a diameter. Each tangent is perpendicular to PQ, and two lines perpendicular to the same line are parallel. Hence the tangents at P and Q are parallel to each other (line \(l \parallel\) line \(m\)).

(Note: a picture cannot be shown here; in the examination the figure must actually be drawn with ruler and compass, labelled as described, and the construction arcs must be kept.)