Draw a circle of radius 4 cm draw two tangents to the circle which are perpendicular to each other

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Draw a circle of radius 4 cm draw two tangents to the circle which are perpendicular to each other

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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

Draw a circle of radius 4 cm draw two tangents to the circle which are perpendicular to each other

Analysis:

As shown in the figure,

In ▢AOBC,

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

∠C = 60°             ......[Given]

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

Draw a circle of radius 4 cm draw two tangents to the circle which are perpendicular to each other

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.

Concept: To Construct Tangents to a Circle from a Point Outside the Circle.

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