MathDB

Rhombus

Source: RMO 2004, Grade 7, Problem 1

February 26, 2006

geometryrhombusparallelogramvector

Problem Statement

On the sides

AB,AD

of the rhombus

ABCD

are the points

E,F

such that

AE=DF

. The lines

BC,DE

intersect at

P

and

CD,BF

intersect at

Q

. Prove that: (a)

\frac{PE}{PD} + \frac{QF}{QB} = 1

; (b)

P,A,Q

are collinear. Virginia Tica, Vasile Tica

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