3
$\begingroup$

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 ?

2 Answers 2

4

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.

  • 0
    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.2012-06-09
1

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 $AB=OB-OA=2$.

  • 0
    Thanks Andre.. appreciate the solution , @Jasper tip was more than enough.. Thanks again2012-06-09