Question

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Q.1: From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle is

(A) 7 cm (B) 12 cm

(C) 15 cm (D) 24.5 cm

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Answer 1

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Option (A)

Step - 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=90⁰

So apply Pythogoras theorem to right triangle, OPQ;

OP² = OQ² - PQ²

OP² = 25² - 24²

OP² = 49 cm

OP = √49

OP = 7 cm

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Answer 2

Answer:

Correct option is

A

7cm

In ⊥△OPQ,∠P=90

∴ As per pythagoras theorem,

OP^2+PQ^2 =OQ^2

OP^2+(24)^2 =(25)^2

OP^2 +576=625

OP^2 =625−576

OP^2=49

∴OP=7cm

Step-by-step explanation:

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