Q.3 (B)(3) Draw a circle with radius 4.1 cm. Construct tangents to the circle from a point at a distance 7.3 cm from the centre.

Answer: Construction steps (each tangent will measure about 6 cm).

1. Draw a circle with centre O and radius 4.1 cm.
2. Take a point P such that OP = 7.3 cm.
3. Draw the perpendicular bisector of seg OP and let it meet OP at M.
4. With M as centre and radius MO, draw a circle. It cuts the given circle at A and B.
5. Draw lines PA and PB. These are the required tangents.

Reason: ∠OAP is an angle in a semicircle, so ∠OAP = 90º and PA ⊥ radius OA. Check: PA = \(\sqrt{7.3^2 - 4.1^2} = \sqrt{36.48} \approx 6.0\) cm.