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From a point Q, the length of the tangent to a circle is 24 cm

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 $25$ cm. The radius of the circle is-

7

12

15

24.5

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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

25

cm. The radius of the circle is-

5 mins ago

Discuss this question LIVE

5 mins ago

Text solutionVerified

Given:-

Tangent

= X Y

Point of contact

= B

Length of tangent to the circle,

PQ = 24 c m

And

OQ = 24 c m

Sol:-

Since

X Y

is tangent,

OP ⊥ X Y (∵ Tangent at any point of circle is perpendicular to the radius through point of contact)

∴ ∠ OPQ = 90

Therefore,

△ OPQ

is a right angled triangle,

Using Pythagoras theorem,

OQ^{2} = OP^{2} + PQ^{2}

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

\Rightarrow OP = 625 - 576 = 7 c m

Hence radius of the circle is

7 c m

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Question Text	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-
Answer Type	Text solution:1
Upvotes	150

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-

Text solutionVerified

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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 $25$ cm. The radius of the circle is-