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In the given figure, O is the centre of a circle. PT and PQ ar

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In the given figure, O is the centre of a circle. $PT$ and $PQ$ are tangents to the circle from an external point P. If $∠ TPQ = 7 0^{\circ}$ , find $∠ TRQ$ .

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In the given figure, O is the centre of a circle.

PT

and

PQ

are tangents to the circle from an external point P. If

∠ TPQ = 7 0^{\circ}

, find

∠ TRQ

12 mins ago

Discuss this question LIVE

12 mins ago

Text solutionVerified

Here, O is the centre of circle.

PQ

and

PT

are tangents to the circle from a point

P

R

is any point on the circle.

RT

and

RQ

are joined.

∠ TPQ = 7 0^{\circ}

Now,

Join

TO

and

QO

∠ TOQ = 18 0^{\circ} - 7 0^{\circ} = 11 0^{\circ}

Here,

OQ

and

OT

are perpendicular on

QP

and

TP .

∠ TOQ

is on the centre and

∠ TRQ

is on the rest part.

∠ TRQ = 1/2∠ TOQ = 1/2 (11 0^{\circ}) = 5 5^{\circ}

Therefore ,

∠ TRQ = 55

degrees.

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Question Text	In the given figure, O is the centre of a circle. $PT$ and $PQ$ are tangents to the circle from an external point P. If $∠ TPQ = 7 0^{\circ}$ , find $∠ TRQ$ .
Answer Type	Text solution:1
Upvotes	151

In the given figure, O is the centre of a circle. PT and PQ are tangents to the circle from an external point P. If ∠TPQ=70∘, find ∠TRQ.

Text solutionVerified

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In the given figure, O is the centre of a circle. $PT$ and $PQ$ are tangents to the circle from an external point P. If $∠ TPQ = 7 0^{\circ}$ , find $∠ TRQ$ .