From a point Q the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25cm.The radius of the circle is
(a) 7cm
(b) 12cm
(c) 15cm
(d) 24.5cm
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From a point Q the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25cm.The radius of the circle is
(a) 7cm
(b) 12cm
(c) 15cm
(d) 24.5cm
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Answer:
Let QP be the tangent, such that, Point of contact is P.
Length of the tangent to a circle = 24cm
$$PQ=24cm$$
Let O be the centre of the circle.
OQ=25cm
We have to find the radius OP
Since QP is tangent
OP perpendicular to QP (Since, Tangent is Perpendicular to Radius at the point of contact)
So, ∠OPQ=90
∘
So apply Pythogoras theorem to right triangle, OPQ;
OP
2
=OQ
2
−PQ
2
OP
2
=25
2
−24
2
OP
2
=49cm
OP=
49
OP=7cm
option A is the answer
Step-by-step explanation:
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Answer:
Option. (a) 7 cm.
Step-by-step explanation:
Let QP be the tangent, such that, Point of contact is P.
Length of the tangent to a circle = 24cm
$$PQ=24cm$$
Let O be the centre of the circle.
OQ=25cm
We have to find the radius OP
Since QP is tangent
OP perpendicular to QP (Since, Tangent is Perpendicular to Radius at the point of contact)
So, ∠OPQ=90
∘So apply Pythogoras theorem to right triangle, OPQ;
OP^2 = OQ^2 - PQ^2
OP^2 = 25^2 - 24^2
OP^2 = 49cm
OP =
OP = 7 cm.
option A is the answer.