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°

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°.

☛ Related Questions:

• If tangents PA and PB from a point P to a circle with center O are inclined to each other at angle of 80°, then ∠POA is equal to(A) 50°(B) 60°(C) 70°(D) 80°
• Prove that the tangents drawn at the ends of a diameter of a circle are parallel.
• Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre.
• The length of a tangent from a point A at distance 5 cm from the centre of the circle is 4 cm. Find the radius of the circle