Question

Draw a circle having radius 3 cm.Draw a chord XY of length 5 cm .Draw tangents at points X and Y without using the centre.

Answer 1

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