Question

In the given figure, the length of $AB$, if $\mathrm{OA}=5\mathrm{cm}$ and $\mathrm{OC}=3\mathrm{cm}$ is

• A. $4cm$
• B. $5cm$
• C. $7cm$
• D. $8cm$

Answer 1

The correct option is D

$8cm$

Step 1: Explanation for correct option

Option (D) $8cm$

By applying Pythagoras theorem in triangle $∆AOC$ we get,

$\begin{array}{rcl}{\mathrm{AC}}^2& =& {\mathrm{OA}}^2-{\mathrm{OC}}^2\\ & =& 25-9=16\\ & \Rightarrow & \mathrm{AC}=4cm\end{array}$

Since $OC\perp AB$

$\Rightarrow AB$ is twice $AC$.

$\Rightarrow \mathrm{AB}=2\times \mathrm{AC}=2\times 4=8\mathrm{cm}$

Hence the length of $AB=8cm$

Hence, option (D) is the correct answer.