Asked in: July 2025 board paperDraw a circle with centre O of 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: The tangents at M and N are the lines perpendicular to radii OM and ON; they meet at a point outside the circle.

Steps of construction:

1. Draw a circle with centre O and radius 3.4 cm.
2. Take any point M on the circle. With M as centre and radius 5.7 cm, draw an arc cutting the circle at N. Draw chord MN.
3. Draw rays OM and ON.
4. At M draw line l perpendicular to ray OM, and at N draw line m perpendicular to ray ON.
5. Lines l and m are the required tangents. They intersect at a point T outside the circle.

[Figure: circle with centre O, radius 3.4 cm; chord MN = 5.7 cm; radii OM and ON; tangent l at M and tangent m at N meeting at T.]

Observation: chord MN (5.7 cm) is shorter than the diameter (6.8 cm), so the tangents are not parallel; they meet at T and TM = TN.