Complete square:


Circle has center O(2,3) and radius 



∠OQA looks like a right angle. That will be the case if
the slopes of OQ and OA are negative reciprocals.  So let's
find out if OQ and OA are perpendicular:

Slope of OQ:


where (x1,y1) = O(2,3)
and where (x2,y2) = (5,5)




Slope of OA:


where (x1,y1) = O(2,3)
and where (x2,y2) = A(4,0)




The slopes are negative reciprocals so ∠QQA = 90°

Edwin