2024 AMC 12B Problems/Problem 24
Problem 24
What is the number of ordered triples of positive integers, with
, such that there exists a (non-degenerate) triangle
with an integer inradius for which
,
, and
are the lengths of the altitudes from
to
,
to
, and
to
, respectively? (Recall that the inradius of a triangle is the radius of the largest possible circle that can be inscribed in the triangle.)