1970 Canadian MO Problems/Problem 2
Problem
Given a triangle with angle
obtuse and with altitudes of length
and
as shown in the diagram, prove that
. Find under what conditions
.
Solution
There is, in fact, no equality case: . In triangle
, we have
since it is a right triangle. Since angle
is obtuse we have
, or
. Then
, or
. Here we can use the fact that
and
are base-altitude pairs so
. Therefore
, so
.