Good evening ,
Explanation:
Using Pythagorean theorem in both right triangles PRQ and PRS we can prove that segment RQ ≅ segment RS
then R is a point of the mediator of segment QS
and since PQ = PS then P also is a point of the mediator of segment QS
finally line PR is the mediator of the segment QS
therefore the line PR passes through the midpoint of segment QS.
:)