MathDB

Right-angled triangle and maximal area

Source: Moldavian TST_1, Problem 2

March 6, 2006

geometryanalytic geometrytrigonometrygeometry proposed

Problem Statement

Consider a right-angled triangle

ABC

with the hypothenuse

AB=1

. The bisector of

\angle{ACB}

cuts the medians

BE

and

AF

P

and

M

, respectively. If

{AF}\cap{BE}=\{P\}

, determine the maximum value of the area of

\triangle{MNP}