Question

Draw a circle of suitable radius and draw a chord XY of length 4.6 cm. Draw tangents at point X and Y without using centre.

Answer 1

Steps of construction:
1. Draw a circle of any radius (should be more than 2.3 cm, otherwise a chord of 4.6 cm will not be possible to draw).
2. Take a point X on the circle and draw chord XY of length 4.6 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.