Tp and tq are two tangents to a circle with centre o so that angle poq 110⁰ then angle ptq is

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In the given figure, if TP and TQ are the two tangents to a circle with centre O so that ∠POQ = 110°, then ∠PTQ is equal to

It is given that TP and TQ are tangents.

Therefore, radius drawn to these tangents will be perpendicular to the tangents.

Thus, OP ⊥ TP and OQ ⊥ TQ

∠OPT = 90º

∠OQT = 90º

In quadrilateral POQT,

Sum of all interior angles = 360°

∠OPT + ∠POQ +∠OQT + ∠PTQ = 360°

⇒ 90°+ 110º + 90° +∠PTQ = 360°

⇒ ∠PTQ = 70°

Hence, alternative 70° is correct.

Concept: Number of Tangents from a Point on a Circle

  Is there an error in this question or solution?

From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle is(A) 7 cm      (B) 12 cm

(C) 15 cm    (D) 24.5 cm.

Since, the tangent at any point of a circle is perpendicular to the radius through the point of contact