Question

In figure if TP and TQ are the two tangents to a circle with centre O so that ∠POQ = 110°, then find the value of ∠PTQ.

Answer 1

PT amd QT are tangents to the circle with centre O.
∴ OP ⊥ PT and OQ ⊥ QT
i.e., ∠POQ = 110°, ∠OPT = 90° ∠OQT = 90°
In quad OPTQ we have,
∠POQ + ∠OPT + OQT + ∠PTQ = 360°
∠PTQ = 360° – (110° + 90° + 90°)
∠PTQ = 360° – 290°
∠PTQ = 70°