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
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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°
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