Draw a circle with centre P and radius 3.5 cm. Take point Q at a distance 8 cm from the centre. Construct tangents to the circle from point Q.

Answer: Rays QA and QB are the required tangents; each is about 7.2 cm long.

Rough figure: a circle with centre P; external point Q with PQ = 8 cm; midpoint M of PQ; a circle with centre M through P and Q cutting the given circle at A and B; tangents QA and QB.

Steps of construction:

1. Draw a circle with centre P and radius 3.5 cm.
2. Take point Q such that PQ = 8 cm and draw seg PQ.
3. Draw the perpendicular bisector of seg PQ; let it meet PQ at M (PM = MQ = 4 cm).
4. With M as centre and radius MP, draw a circle. Let it cut the given circle at A and B.
5. Draw rays QA and QB. These are the required tangents.

Final figure (as drawn): circle with centre P (radius 3.5 cm); seg PQ = 8 cm with its perpendicular-bisector arcs and midpoint M; the circle with centre M through P and Q; points A and B on the given circle; rays QA and QB; radii PA and PB may be drawn dotted.

Reason: \(\angle QAP\) is an angle inscribed in a semicircle, so \(\angle QAP = 90^\circ\), i.e. QA \(\perp\) radius PA, so QA is a tangent; similarly QB. Check: \(QA = \sqrt{8^2 - 3.5^2} = \sqrt{51.75} \approx 7.2\) cm.

(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.)