Draw a circle of diameter 6.4 cm. Take a point R at a distance equal to its diameter from the centre. Draw tangents from point R.

Answer: Radius = 3.2 cm, OR = 6.4 cm. The circle on OR as diameter cuts the given circle at A and B; RA and RB are the tangents (each ≈ 5.5 cm).

Steps of construction:

1. Draw a circle with centre O and radius 3.2 cm (diameter 6.4 cm).
2. Mark point R such that OR = 6.4 cm and draw seg OR.
3. Draw the perpendicular bisector of seg OR; let it cut OR at M (the midpoint).
4. With centre M and radius MO, draw a circle. Name the points where it cuts the given circle as A and B.
5. Draw lines RA and RB. These are the required tangents.

Why it works: \(\angle OAR\) and \(\angle OBR\) are angles inscribed in a semicircle (diameter OR), so each is \(90^\circ\). A line perpendicular to a radius at its outer end is a tangent.

Check: each tangent segment \(= \sqrt{6.4^2 - 3.2^2} \approx 5.5\) cm, and the two tangent segments are equal.

Here \(\sin\angle ORA = \dfrac{3.2}{6.4}=\dfrac12\), so \(\angle ORA = 30^\circ\) and the tangents make \(60^\circ\) with each other.