Let O=(0,0), Q=(13,4), A=(a, a), B=(b, 0), where a and b are positive real numbers with b \geq a. The point Q is on the line segment A B.
(a) Determine the values of a and b for which Q is the midpoint of A B.
(b) Determine all values of a and b for which Q is on the line segment A B and the triangle O A B is isosceles and right-angled.
(c) There are infinitely many line segments A B that contain the point Q. For how many of these line segments are a and b both integers?