Question

Draw a circle of radius 2.7 cm and draw chord PQ of length 4.5 cm .Draw tangents at points P and Q without using centre.

Answer 1

Steps of construction:
1. Draw a circle of radius 2.7 cm.
2. Draw chord PQ of length 4.5 cm.
3. Take two points X and Y on the alternate arc of PDQ other than P and Q.
4. Join XP, XQ, QY and YP. So, $\angle \mathrm{PXQ}$ and $\angle \mathrm{PYQ}$ are formed.
5. Draw ray PA making an angle equal to $\angle \mathrm{PYQ}$ using PQ as one side and vertex P.
6. Similarly, draw ray QB making an angle equal to $\angle \mathrm{PXQ}$ using PQ as one side and vertex Q.
7. The lines (l and m) containing rays PA and QB are the required tangents.