Point \(P\) sits inside an angle \(O\) of \(60^\circ,\) as shown below.
Link to image ---> https://latex.artofproblemsolving.com/8/3/0/830265669c9c3e7ccc70574d2b1693251fc4e4c4.png
Line segments \(\overline{PA}\) and \(\overline{PB}\) are drawn so they are perpendicular to the two rays forming angle \(O\) as shown. Given \(OA = a\) and \(OB = b,\) find the distance \(OP\) in terms of \(a\) and \(b\).
Thank you!
