Question

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

Answer 1

Given that PQ = 24 cm and OQ = 25 cm.

To find OP, apply Pythagoras theorem for $△$OPQ.

${OP}^2+{QP}^2={OQ}^2$

${OP}^2+{24}^2={25}^2$

${OP}^2=625-576=49$

$\Rightarrow OP=7\text{cm}$