In the given figure M is the center of the circle, OA=x and AB=1 unit.PA is perpendicular to OB. Prove that PA represents the square root of x.

Dear Student

OB = x + 1 = diameter of circle

radius = ( x+1)/2
length CA = x –radius = (x-1)/2
PC = radius = (x+1)/2
Now, By Pythagoras theorem in Triangle PAC
PC² = AP² + AC²
PA = √x
Thanks

Approved