MathDB
Right-angled triangle

Source: Romanian NMO 2007, 7th grade, problem nr. 2

July 11, 2008
functiongeometrytrapezoid

Problem Statement

Consider the triangle ABC ABC with m(\angle BAC \equal{} 90^\circ) and AC \equal{} 2AB. Let P P and Q Q be the midpoints of AB AB and AC AC,respectively. Let M M and N N be two points found on the side BC BC such that CM \equal{} BN \equal{} x. It is also known that 2S[MNPQ] \equal{} S[ABC]. Determine x x in function of AB AB.
Back to ProblemsView on AoPS