Question

Draw a circle with centre P and radius 3.1 cm.Draw a chord MN of length 3.8 cm .Draw tangents to the circle through points M and N.

Answer 1

Steps of construction:
1. Draw a circle of radius 3.1 cm.
2. Draw chord MN of length 3.8 cm.
3. Take two points R and Q on the alternate arc of MND other than M and N.
4. Join MR, MQ, NR and NQ. So, $\angle \mathrm{MRN}$ and $\angle \mathrm{MQN}$ are formed.
5. Draw ray MA making an angle equal to $\angle \mathrm{MQN}$ using MN as one side and vertex M.
6. Similarly, draw ray NB making an angle equal to $\angle \mathrm{MRN}$ using MN as one side and vertex N.
7. The lines (l and m) containing rays MA and NB are the required tangents.