KV AFS AVADI - SECONDARY SECTION QUESTION BANK AND HOME WORKS

Question 1:

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.
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.

Hence, alternative (A) is correct.