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
Share
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
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
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
o
[from (2) and (3)]
or, 180
o
−2∠OPQ+∠PTQ=180
o
∴ 2∠OPQ=∠PTQ−−−− proved