Question

Attached In figure-III, from an external point T, two tangents TP and TQ are drawn to a circle with centre O and radius r. If OT = 2r, show that ∠ = ∠ = 300 .

Answer 1

Answer:

the external point P of a circle with Centre O.

∠ OPQ = 30°

In the figure Join OP, OQ & PQ

∠ OPT = ∠ OQT = 90°

[We know that the tangent at any point of a circle is perpendicular to the radius through the point of contact.]

In ∆OPQ,

OP = OQ [ radius of the circle]

∠OPQ = ∠OQP = 30°

[Angles opposite to equal sides of a ∆ are equal]

∠TQP = ∠OQT - ∠OQP

∠TQP = 90° - 30°

∠TQP = 60°

Hence, the the measure of ∠TQP is 60°.

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