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 \(b\). Explaining in depth would be greatly appreciated.
Thank you!