Answer: Construction steps (each tangent is about 4.5 cm long).
- Draw a circle with centre O and radius 3.5 cm.
- Mark a point P on the plane of the circle such that OP = 5.7 cm.
- Draw the perpendicular bisector of seg OP; let it meet seg OP at M.
- With M as centre and radius MO, draw a circle. It intersects the given circle at two points, say A and B.
- Draw rays PA and PB. These are the required tangents from P to the circle.
Reason: A and B lie on the circle with diameter OP, so ∠OAP = ∠OBP = 90º; hence PA and PB are perpendicular to the radii OA and OB at the points of contact.
Check: PA = PB = \(\sqrt{OP^2 - OA^2} = \sqrt{5.7^2 - 3.5^2} = \sqrt{32.49 - 12.25} = \sqrt{20.24} \approx 4.5\) cm.
