If ap and AQ are the two tangents to a circle with centre O so that POQ = 110 then paq

Solution:

The tangent at any point of a circle is perpendicular to the radius at the point of contact.

In the above figure, OPTQ is a quadrilateral and ∠P and ∠Q are 90°

The sum of the interior angles of a quadrilateral is 360°.

Therefore,  in OPTQ,

∠Q + ∠P + ∠POQ + ∠PTQ = 360°

90° + 90° + 110° + ∠PTQ = 360°

290° + ∠PTQ = 360°

∠PTQ = 360° - 290°

∠PTQ = 70°

Thus, option (B) 70° is the correct answer.

☛ Check: NCERT Solutions Class 10 Maths Chapter 10

Video Solution:

In Fig. 10.11, if TP and TQ are the two tangents to a circle with centre O so that ∠ POQ = 110°, then ∠ PTQ is equal to (A) 60° (B) 70° (C) 80° (D) 90°

Maths NCERT Solutions Class 10 Chapter 10 Exercise 10.2 Question 2

Summary:

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 70°.

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If AP and AQ are the two tangents to a circle with centre 'O' so that ∠ P O Q=120∘, then ∠ P A Q is equal toB. 60∘C. 80∘D. 90∘