Fewpal
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(A) 7 cm (B) 12 cm (C) 15 cm (D) 24.5 cm

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Solution:

The line drawn from the centre of the circle to the tangent is perpendicular to the tangent.

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

∴ OP ⊥ PQ
also, ΔOPQ is right angled.
OQ = 25 cm and PQ = 24 cm (Given)

By Pythagoras theorem in ΔOPQ,

OQ2 = OP2 + PQ2
⇒ (25)= OP2 + (24)2

⇒OP2 = 625 - 576

⇒OP2 = 49

⇒OP = 7 cm

Option (A) is correct

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