Relation between ##d## and ##\theta##

[Adel Makram]

I wish to find a closed form relation between $\theta$ and $d$ in the attached figure as a function of $r$, the radius of the circle and $s$ the distance from the point $p$ to the center.
Thank you.

 

[berkeman]

Can you please show your work so far? What part are you having trouble with?

Is this question for schoolwork?

 

[Adel Makram]

Can you please show your work so far? What part are you having trouble with?

Is this question for schoolwork?

Just right now, I had insight for how to solve it :)
$s^2=r^2+d^2+2 d r cos (a)$
But $a+\theta=\pi/2$.
$s^2=r^2+d^2+2 d r cos (\pi/2 -\theta)$
rearranding, gives a relation between $d$ and $\theta$.