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
Given:
OQ = 25 cm
PQ = 24 cm
Property: The tangent at a point on a circle is at right angles to the radius obtained by joining center and the point of tangency.
By above property, ∆POQ is right-angled at ∠OPQ.
Therefore,
By Pythagoras Theorem in ∆POQ,
OP2 + PQ2 =OQ2
⇒ OP2 = OQ2 – PQ 2
⇒ OP= √( OQ2 – PQ 2)
⇒ OP= √(252 – 242)
⇒ OP= √(625 – 576)
⇒ OP = √49 cm
⇒ OP = 7 cm
Hence, OP = 7 cm