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.

Solution

Since, the tangent at any point of a circle is perpendicular to the radius through the point of contact

therefore space space space space space space OQ squared space equals space OP squared space plus space PQ squared space space space space space space space space space left curly bracket By space Pythagoras space theorem right square bracket rightwards double arrow space space space space space space left parenthesis 25 right parenthesis squared equals OP squared plus 576 rightwards double arrow space space space space space space OP squared space equals space 625 minus 576 rightwards double arrow space space space space space space OP squared space equals space 49 rightwards double arrow space space space space space space OP space equals space square root of 49 space equals space 7 space cm rightwards double arrow space space space space space space Radius space of space the space circle space is space 7 space cm.

Hence, the correct option is (A) 7 cm.

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