Question

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

Fig. 10.11

• A. 60°
• B. 70°
• C. 80°
• D. 90°

Answer 1

The Correct Option is B

It is given that \(\text {TP}\) and \(\text {TQ}\) are tangents.
Therefore, radius drawn to these tangents will be perpendicular to the tangents.
Thus, \(\text {OP ⊥ TP }\) and \(\text {OQ ⊥ TQ}\)
\(∠OPT = 90º\)
\(∠OQT = 90º\)
In quadrilateral \(POQT\),
Sum of all interior angles \(= 360º\)
\(∠OPT + ∠POQ +∠OQT + ∠PTQ = 360º\)
\(⇒ 90º + 110º + 90º + PTQ = 360º\)
\(⇒ PTQ = 70º\)

Hence, the correct option is (B): \(70º\)