Circles/Arcs. Please Help!

[ninax3]

Ok, in the Circle below, C is the center of the circle. CB = 8. AB = 6. Find the measure of arc AB.

Thanks!
P.S.- is there like a formula to do these type of questions or something to remember how to do it with? Because I don't really get this stuff.. :?

 

[tkhunny]

l(CA) = 8.

This gives an isosceles triangle ABC.

Can you calculate the angle at C?

 

[ninax3]

It doesn't give the angle measure for C or any other angle.

 

[pka]

The point is the as a central angle \(\displaystyle m(arc(AB)) = m\angle ACB.\)

Now in the diagram the line CD is the perpendicular bisector of AB.
Therefore, the length of DB is 3. Moreover, \(\displaystyle m\angle ACB = 2m\angle DCB\).

We know that \(\displaystyle m\angle DCB = \arcsin \left( {\frac{3}{8}} \right)\).
Now you finish the problem.

 

[ninax3]

Ok thanks. :]