Draw a circle with centre O and radius 3.5 cm. Take point P at a distance 5.7 cm from the centre. Draw tangents to the circle from point P.

Answer: Draw the circle with diameter OP; it cuts the given circle at A and B. PA and PB are the tangents (each ≈ 4.5 cm).

Steps of construction:

1. Draw a circle with centre O and radius 3.5 cm.
2. Mark point P such that OP = 5.7 cm and draw seg OP.
3. Draw the perpendicular bisector of seg OP; let it cut OP 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 PA and PB. These are the required tangents.

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

Check: each tangent segment \(= \sqrt{5.7^2 - 3.5^2} \approx 4.5\) cm, and the two tangent segments are equal.