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 .