Math, asked by devananda19, 7 months ago

o is the centre of the circle .PT and PQ are tangents to the circle from an external point P .if angle TPQ=70 degree. find angleTRQ​

Answers

Answered by Anonymous
111

CorrecT QuestioN :-

O is the centre of the circle .PT and PQ are tangents to the circle from an external point P .if angle TPQ=70 degree. find ∠TOQ [ since R is no where mentioned in the given Question . ]

GiveN :-

  • O is the centre of the circle .
  • PT and PQ are tangents from a external point P .
  • Value of ∠ TRQ = 70° .

To FinD :-

  • The value of ∠TRQ .

AnsweR :-

[ For figure refer to the attachment : ]

We know that radius is perpendicular to tangent at the point of contact . Hence here ,

  • ∠OQP = ∠OTQ = 90°
  • ∠QPT = 70° .

Here , we can see that OQPT is a quadrilateral . And angle sum property of a quadrilateral is 360° . Hence here ;

⇒ ∠OQP +∠OTQ + ∠QPT +∠TOQ = 360°

⇒ ∠TOQ + 90° + 90° + 70° = 360°

⇒ ∠TOQ + 250° = 360°

⇒ ∠TOQ = 360° - 250°

∠TOQ = 110°

Hence the value of ∠TOQ is 110°

\Large{\boxed{\boxed{\pink{\sf \red{\bigstar}\: Value\: of\;\angle TOQ \:is\:110^{\circ}}}}}

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