Question

In the figure ‘o’ is the centre of the circle. OM = 3cm and AB = 8cm. Find the radius of the circle.
a)5 cm

b)4 cm

c)15 cm

 d)8 cm

Answer 1

Hint: OM is the perpendicular from the centre of the chord AB. Thus OM divides AB into half. Joint OA and take it as the radius we need to find. Using Pythagora's theorem in\[\vartriangle OAM\], find the length of OA.

Complete step-by-step answer:
We have been given a circle with centre ‘o’.

We need to find the radius of the circle. From the figure let us join OA and mark it as the radius of the given circle. Now we need to find the value of OA.

We have been given OM = 3cm and AB= 8cm.

We know that perpendicular from the centre of the circle to the chord bisect the chord. Now here OM is a perpendicular from the angle of the circle to the chord AB.


Thus \[AM=\dfrac{1}{2}AB\] (from the figure)

                  \[=\dfrac{1}{2}\times 8=4cm\]

Hence we got AM = 4cm.

Now \[\vartriangle OMA\]is a right triangle as\[OM\bot AB\].


By Pythagoras theorem, we can say that


\[O{{M}^{2}}+A{{M}^{2}}=O{{A}^{2}}\]


Put the values of OM = 3cm and AM = 4cm.


\[\begin{align}

  & \therefore O{{A}^{2}}={{\left( 3 \right)}^{2}}+{{\left( 4 \right)}^{2}} \\

 & \\

 & =9+6=25 \\

 & \\

 & OA=\sqrt{25}=5cm \\

\end{align}\]


Hence we got OA = 5cm that is radius of the given circle is 5cm

\[\therefore \] Option (a) is the correct answer.


Note: You can also consider OB as radius, then AM = BM = 4cm.

Assume \[\vartriangle OMB\]and by Pythagoras theorem you will get OB = 5cm.

Here OA and OB both are the radius of the given circle. So,

OA = OB = 5cm.