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Median, altitude relationships

Source: Pan African MO 2012 Day 2 Q3

October 14, 2012

trigonometrygeometry proposedgeometry

Problem Statement

(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

.

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