Question

From a point Q the length of the tangent to a circle is 24cm and  the distance of Q from the center is 25cm. The radius of the circle is​

Answer 1

Step-by-step explanation:

Let O be the centre of the circle.

Given that,

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

OP = 7

Therefore, the radius of the circle is 7 cm.

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