# How do I calculate a point's coordinates on a circle’s circumference

I have got a circle with radius $r$ and center point $c_x$ and $c_y$.

Known values: - $c_x$ and $c_y$ - $r$ - length $AR_a$ - length $BR_b$

Angle between point $A$ and the radius $r$ is unknown and angle between $B$ and the radius $r$ is unknown. Is it posible to get coordinates for $A$ and $B$ using any formula?

Thanks a lot in advance.

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The radius $r$ appears both in the list of knowns and unknowns... What have you tried ? Where do you encounter a difficulty ? – Tom-Tom Feb 13 '14 at 9:36
It's angle between radius and A is unknown and angle between radius and B is unknown. I'll try to write it in different way – Peter O. Feb 13 '14 at 9:41
So you mean the unknown is the angle $\widehat{ACR_a}$ where $C$ is the center ? That could be a better way to write it. Could you edit your question and tell us what you have tried, this would help to answer at the appropriate level. – Tom-Tom Feb 13 '14 at 9:44
Yes, I'm sorry for my writting skills :( @Hagen von Eitzen has provided the best answer. – Peter O. Feb 13 '14 at 9:46

Use Pythagoras to obtain the vertical distance $\sqrt{r^2-|AR_a|^2}$