Question

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

Answer 1

The line drawn from the centre of the circle to the tangent is perpendicular to the tangent.

$\therefore OP\perp PQ$
Also, $\Delta$ OPQ is right angled.
OQ = 25 cm and PQ = 24 cm (Given)
By Pythagoras theorem in $\Delta$ OPQ,
$O{Q}^2=O{P}^2+P{Q}^2\Rightarrow (25{)}^2=O{P}^2+(24{)}^2\Rightarrow O{P}^2=625-576\Rightarrow O{P}^2=49\Rightarrow OP=7cm$