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Write the steps of construction for drawing a pair of tangents to a circle of radius 3 cm , which are inclined to each other at an angle of 60° .

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Steps of Construction

Step 1: Draw a circle with center O and radius 3c m.

Step 2: Draw any diameter AOB of the circle.

Step 3: Construct ∠BOC = 60° such that radius OC cuts the circle at C.

Step 4: Draw \(AM \perp AB\) and \(CN \perp OC.\) Suppose AM and CN intersect each other at P.

Here, AP and CP are the pair of tangents to the circle inclined to each other at an angle of 60°.

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by (403 points)
  • Steps of Construction:
  • Step I: Draw a circle with centre O and radius 3 cm.
  • Step II: Draw any diameter AOB.
  • Step III: Draw a radius OC such that ∠ BOC = 60°.
  • Step V: Let the two perpendiculars intersect each other at P.
  • Step IV: At C, we draw CM ⊥ OC and a

    Justification:
    Since OA is the radius, so PA has to be a tangent to the circle. Similarly, PC is also tangent to the circle.

    ∠APC = 360° – (∠OAP + ∠OCP + ∠AOC)

    = 360° – (90° + 90° + 120°) = 360° – 300° = 60°

    Hence, tangents PA and PC are inclined to each other at an angle of 60°.

    t A, we draw AN ⊥ OA.

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