[obm-l] Geometry Problem

["Paulo Santa Rita" <p_ssr@xxxxxxxxxxx>]

>Hi. Firstly, this is not homework, I actually want this for a bit of
>software I am writing.
>Secondly, while I know it would be better if I worked it out myself, I'd
>rather get the solution than not, even at the price of missing the
>opportunity to brush up my geometry skills.
>
>I am attempting to lay out points on the Poincare projection of the
>hyperbolic plane. I have done up a diagram at
>http://www.users.bigpond.com/pmurray/Math1.gif
>
>I have a unit circle C, with a centre at O.
>I have a radius of that circle r.
>I have another circle D, that intersects C at right angles at a point P and
>that intersects the radius R at point Q.
>
>Angle POr we shall call theta.
>Angle Dr we shall call phi. (that is, the angle between r and the tangent 
>to
>D at Q).
>Distance OQ we shall call d.
>
>1 - given phi and d, what is theta?
>2 - given phi and theta, what is d?
>
>That's all I think I need, although if you feel like working out phi from
>theta and d, feel free.
>
>Please reply to me at pmurray@bigpond.com.
>
>..




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