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In the figure shown if area of circle with center o is 100pi and CA has length of 6 what is length of AB ?enter image description here

I looked around on the web and cant seem to get an idea of what the angles AOC and OCA inside the triangle would be. Any suggestions on how I would go about determining them ?

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up vote 4 down vote accepted

Given that the area of the circle is $100\pi$, its radius $OC$ is $10$. Using Pythagoras Theorem one finds that $OA=8$. From there you may work out $AB$ and use the inverse trigonometric functions to find the angles.

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Thanks for the tip!! that helped. I was aiming for the wrong approach thinking that there might be some rule which defines the angles formed in such a case. – Rajeshwar Jun 9 '12 at 11:41

The angles are not needed. From the area, we find that the radius is $10$. Thus by the Pythagorean Theorem, $OA=\sqrt{10^2-6^2}=8$. But $OB$ is a radius, so $OB=10$, and therefore $AB=OB-OA=2$.

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Thanks Andre.. appreciate the solution , @Jasper tip was more than enough.. Thanks again – Rajeshwar Jun 9 '12 at 13:57

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