Question

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​

Answer 1

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 2

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 =

$\sqrt{49}$

OP = 7 cm.

option A is the answer.