AMC 12B 2024 Problem 24. Ordered Triples of Altitudes and Integer Inradius

What is the number of ordered triples (a, b, c) of positive integers, with a less than= b less than= c less than= 9, such that there exists a (non-degenerate) triangle ABC with an integer inradius for which a, b, and c are the lengths of the altitudes from A to BC, B to AC, and C to AB, respectively? (Recall that the inradius of a triangle is the radius of the largest possible circle that can be inscribed in the triangle.) (A) 2(B) 3(C) 4(D) 5(E) 6