Q. 14.4( 304 Votes )
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
Let O be the centre of the circle.
OQ = 25cm and PQ = 24 cm
As the radius is perpendicular to the tangent at the point of contact,
Therefore, OP ⊥ PQ
Applying Pythagoras theorem in ΔOPQ, we obtain
OP2 + PQ2 = OQ2
OP2 + 242 = 252
OP2 = 625 - 576
OP2 = 49
Therefore, the radius of the circle is 7 cm.
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