Math, asked by agarwalniharika673, 3 months ago

line TP and TQ are tangents from an external point of a circle. if the pine that intersects at the middle point of PQ from T is 4 cm , and the length of the chord is 2 cm .Find the area of the circle​

Answers

Answered by farhaanaarif84
9

Refer image

We know that length of taughts drawn from an external point to a circle are equal

∴ TP=TQ−−−(1)

4∴ ∠TQP=∠TPQ (angles of equal sides are equal)−−−(2)

Now, PT is tangent and OP is radius.

∴ OP⊥TP (Tangent at any point pf circle is perpendicular to the radius through point of cant act)

∴ ∠OPT=90

o

or, ∠OPQ+∠TPQ=90

o

or, ∠TPQ=90

o

−∠OPQ−−−(3)

In △PTQ

∠TPQ+∠PQT+∠QTP=180

o

(∴ Sum of angles triangle is 180

o

)

or, 90

o

−∠OPQ+∠TPQ+∠QTP=180

o

or, 2(90

o

−∠OPQ)+∠QTP=180

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[from (2) and (3)]

or, 180

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−2∠OPQ+∠PTQ=180

o

∴ 2∠OPQ=∠PTQ−−−− proved

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