Question

In the given figure, chord $AB$ subtends $\angle AOB$ is equal to $60°$ at the centre of the circle. If $OA=5cm$, then length of $AB$ (in $cm$) is

• A. $\frac{5}{2}cm$
• B. $\frac{5\sqrt{3}}{2}cm$
• C. $5cm$
• D. $\frac{5\sqrt{3}}{4}cm$

Answer 1

The correct option is C

$5cm$

Step 1: Equal sides have equal angles in triangle

As per the data given in the above question are as follows,

$\angle AOB=60°$

$OA=5cm$,

We have to determine the length of $AB.$

We know that $OA$ and $OB$ are the radius of the circle,

Therefore $OA=OB$

Where,

$$\begin{gathered} OA=5cm \\ OB=5cm \end{gathered}$$

So.

$\angle A=\angle B$

Step 2- Angle sum property of triangle.

Now consider the triangle $∆OAB$

$\begin{array}{rcl}\angle A+\angle B+\angle O& =& 180°\\ 2\angle A+60°& =& 180°\\ \angle A& =& 60°\end{array}$

When $\angle A=\angle B=\angle O=60°$

Therefore triangle $∆OAB$ is an equilateral triangle.

So, $AB=5cm$

Hence the length of $AB$ is $5cm$.

Hence option (C) is correct.