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

• A. $7cm$
• B. $12cm$
• C. $15cm$
• D. $24.5cm$

Answer 1

The correct option is A

$7cm$

Explanation for the correct option

Let $P$ be the point of contact of the tangent from $Q$.

Given, $PQ=24cm$ and $OQ=25cm$.

From the figure $OP$ is the radius of the circle

Since $PQ$ is the tangent to the circle, we can say $OP\perp PQ$.

According to Pythagoras theorem,

$$\begin{gathered} {\left(OQ\right)}^2={\left(OP\right)}^2+{\left(PQ\right)}^2 \\ \Rightarrow {\left(OP\right)}^2={\left(OQ\right)}^2-{\left(PQ\right)}^2 \\ ={\left(25\right)}^2-{\left(24\right)}^2 \\ =625-576 \\ =49 \\ \Rightarrow OP=\sqrt{49} \\ \Rightarrow OP=7cm \end{gathered}$$

Hence, the correct option is option A.