Problem
In a square ABCD with side length s, there is a moving point P.
The angle at P is 90 degrees.
Find the minimum value of PC.
Solution
The set-up to the problem is below. The key is to note that the loci of points that form the right angle in question is a circle itself with radius s/2 with center (0,s/2).
Now note that the equation of the line connecting (0,s/2) and C=(s,0) is y=s/2-1/2 x .
If you insert this into the equation for the circle for the loci of points P, we’ll find
So that the distance between this point and C is
