MathDB

Nice Conditions!

Source: Czech-Slovak Match 1996

September 14, 2004

geometrygeometry solved

Problem Statement

The points

E

and

D

lie in the interior of sides

AC

and

BC

, respectively, of a triangle

ABC

. Let

F

be the intersection of the lines

AD

and

BE

.Show that the area of the traingles

ABC

and

ABF

satisfies:

\frac{S_{ABC}}{S_{ABF}} = \frac{\mid{AC}\mid}{\mid{AE} \mid} + \frac{\mid{BC}\mid}{\mid{BD}\mid} - 1

.

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