Draw a circle with radius 3.4 cm. Draw a chord MN of length 5.7 cm in it. Construct tangents at point M and N to the circle.

Answer: Draw radii OM and ON and draw lines perpendicular to them at M and N; these are the tangents (they meet outside the circle).

Steps of construction:

1. Draw a circle with centre O and radius 3.4 cm.
2. Take point M on the circle. With centre M and radius 5.7 cm cut the circle at N. Draw chord MN.
3. Draw rays OM and ON.
4. Through M draw line \(l \perp\) ray OM; through N draw line \(m \perp\) ray ON.
5. Lines \(l\) and \(m\) are the required tangents.

Observation: since MN is not a diameter (5.7 < 6.8), the tangents intersect at a point, say T, outside the circle, and TM = TN (tangent segments from an external point are equal).