CMO 1970 Problem 2

Paper

Given a triangle $ABC$ with angle $A$ obtuse and with altitudes of length $h$ and $k$ as shown in the diagram, prove that $a+h\ge b+k$ . Find under what conditions $a+h=b+k$ .

A

B

C

D

E

h

k

Dataset text AI-MO AoPS. Quoted with source.

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