Question

If TP and TQ are 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°

Answer 1

Correct option is: (B) 70°

\(\because \) OP \(\perp\) PT & OQ \(\perp\) QT.

(Tangent is perpendicular to radius at point of contact)

= \(\angle\) OPT = 90° & \(\angle\) OQT = 90°

\(\because \) Sum of angles in a quadrilateral is 360°.

\(\therefore\) \(\angle\) OPT + \(\angle\) OQT + \(\angle\) OPQ + \(\angle\) PTQ = 360°.

= 90° + 90° + 110° +  \(\angle\) PTQ = 360°.

=  \(\angle\) PTQ = 360°- 290° = 70°.

Answer 2

Correct option is: (B) 70°