Question

If the radii of two concentric circles are $4cm$ and $5cm$, then the length of each chord of one circle which is tangent to the other circle is:

• A. $3cm$
• B. $6cm$
• C. $9cm$
• D. $1cm$

Answer 1

The correct option is B

$6cm$

Explanation for the correct option.

Step $1:$ Defining the given data and making an appropriate diagram

As per given information, consider the figure showing two concentric circles such having radii

$$\begin{gathered} OB=4cm \\ OC=5cm \end{gathered}$$

Step $2:$ Calculate the length of the given chord.

Find the length of the line segment $BC$.

Using Pythagoras Theorem in triangle $OBC$

$$\begin{gathered} {\left(OB\right)}^2+{\left(BC\right)}^2={\left(OC\right)}^2 \\ \Rightarrow {\left(4\right)}^2+{\left(BC\right)}^2={\left(5\right)}^2 \\ \Rightarrow 16+{\left(BC\right)}^2=25 \\ \Rightarrow {\left(BC\right)}^2=9 \\ \Rightarrow BC=\sqrt{9} \end{gathered}$$

Therefore, the length of the line segment $BC$ is $3cm$.

Since $AC$ is the given chord and $OB$ is the perpendicular bisector for $AC$.

Therefore, $AC=2BC$

$\Rightarrow AC=6$

So, the length of each chord of first circle which is tangent to the other circle is $6cm$.

Hence, option $B$ is the correct answer.