Question

In a circle with centre o and radius 6cm if the length of a chord AB is 6 root 3 then angle AOB

Answer 1

Answer:

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Answer 2

Given:

In a circle with centre O and radius 6cm if the length of a chord AB is 6 root 3

To Find:

Find angle AOB

Solution:

First, try to draw a diagram of a circle with the given information to visualize the question in a better way,

Draw a circle and then draw a chord AB from centre O join the lines AO and BO

Now we can observe that the angle it is making from the centre name it as 2theta, then draw a perpendicular to the chord and that perpendicular will divide the chord into two equal parts

Now take the triangle OBC and here we can use trigonometry to find the value of theta, which will go as

$Sin\theta =\frac{BC}{OB}\\=\frac{3\sqrt{3} }{6}\\=\frac{\sqrt{3} }{2}\\\theta=60^{\circ}$

so the angle AOB is twice of theta then,

AOB=2*60=120

Hence, the angle AOB is 120 degrees.