Question

Draw a circle with radius 4 cm and construct two tangents to a circle such that when those two tangents intersect each other outside the circle they make an angle of 60° with each other

Answer 1

Analysis:

As shown in the figure,

In ▢AOBC,

∠A = ∠B = 90°     ......[Tangent theorem]

∠C = 60°             ......[Given]

∴ ∠O = 120°       ......[Remaning angle of ▢AOBC]

Steps of constructions:

1. With centre O, draw a circle of radius 4 cm.
2. Take any point A on the circle and draw ray OA.
3. Draw line l ⊥ ray OA at point A.
4. Draw ray OB such that ∠AOB = 120°. Point B must be on the circle.
5. Draw line m ⊥ ray OB at point B.
   l and m are the required tangents.