Question
If TP and TQ are two tangents to a circle with center O such that ∠POQ=110∘, then, ∠PTQ is equal to:
Answer: Option B
:
B
Given that∠POQ=110∘
Note that ∠OQT=∠OPT=90∘
(∵ A tangent at any point of a circle is perpendicular to the radius at the point of contact)
Also, ∠TQO+∠QOP+∠OPT+∠PTQ=360∘(∵Sum of interior angles of a quadrilateral is 360 degrees)
⟹∠PTQ=360∘–90∘–90∘–110∘
⟹∠PTQ=70∘
∴∠PTQ=70∘
Was this answer helpful ?
:
B
Given that∠POQ=110∘
Note that ∠OQT=∠OPT=90∘
(∵ A tangent at any point of a circle is perpendicular to the radius at the point of contact)
Also, ∠TQO+∠QOP+∠OPT+∠PTQ=360∘(∵Sum of interior angles of a quadrilateral is 360 degrees)
⟹∠PTQ=360∘–90∘–90∘–110∘
⟹∠PTQ=70∘
∴∠PTQ=70∘
Was this answer helpful ?
More Questions on This Topic :
Latest Videos
Latest Test Papers
Submit Solution