Question

construct a pair of Tangent to a circle of Radius 3.5cm such that angle between Radio is 120degree

Answer 1

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Answer 2

Follow the given steps to construct a pair of tangents.

Step 1: Take a point O on the plane and draw a circle of radius OA = 3.5 cm

Step 2: Draw ∠AOB = ∠AOC = 30° at O.

Step 3: Draw BX ⊥ OB and CX ⊥ OC at B and C respectively. BX and CS intersects at x.

Here, BX and CX are two tangents to the circle inclined to each other at 120°.

Justification:

∠XOB = 30°

∠OBX = 90°

In ΔBOX,

∠XOB + ∠OBX + ∠BXO = 180°

∴ 30° + 90° + ∠BXO = 180°

⇒ ∠BXO = 180° – 120° = 60°

Similarly, ∠CXO = 60°

∴ ∠BXC = ∠BXO + ∠CXO = 60° + 60° = 120°