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19/06/2021 11:18 am
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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
(A) 7 cm
(B) 12 cm
(C) 15 cm
(D) 24.5 cm
1 Answer
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19/06/2021 11:23 am
Correct option:(A) 7 cm
Explanation:
OP is perpendicular to PQ i.e. OP ⊥ PQ
From the above figure, it is also seen that △OPQ is a right angled triangle.
It is given that
OQ = 25 cm and PQ = 24 cm
By using Pythagoras theorem in △OPQ,
OQ2 = OP2 + PQ2
(25)2 = OP2 + (24)2
OP2 = 625 - 576
OP2 = 49
OP = 7 cm
So, 7 cm is the radius of the given circle.