MathDB

Romania District Olympiad 2001 - VII Grade

Source:

March 12, 2011

symmetrygeometryparallelogramgeometry proposed

Problem Statement

Consider a triangle

\Delta ABC

and three points

D,E,F

such that:

B

and

E

are on different side of the line

AC

,

C

and

D

are on different sides of

AB

,

A

and

F

are on the same side of the line

BC

. Also

\Delta ADB \sim \Delta CEA \sim \Delta CFB

. Let

M

be the middle point of

AF

. Prove that:
a)

\Delta BDF \sim \Delta FEC

. b)

M

is the middle point of

DE

.
Dan Branzei

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