PAMO 2012 Problem 6

Day 2

(i) Find the angles of $\triangle ABC$ if the length of the altitude through $B$ is equal to the length of the median through $C$ and the length of the altitude through $C$ is equal to the length of the median through $B$ .

(ii) Find all possible values of $\angle ABC$ of $\triangle ABC$ if the length of the altitude through $A$ is equal to the length of the median through $C$ and the length of the altitude through $C$ is equal to the length of the median through $B$ .

Dataset text AI-MO AoPS. Quoted with source.

Official text: Pan-African Mathematics Olympiad 2012 official paper, page 1.

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