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AO/OD= AE/EC+AF/FB

Source: 2001 Estonia National Olympiad Final Round grade 11 p3

March 12, 2020

geometryratio

Problem Statement

Points

D,E

and

F

are taken on the sides

BC,CA,AB

of a triangle

ABC

respectively so that the segments

AD, BE

and

CF

intersect at point

O

. Prove that

\frac{AO}{OD}= \frac{AE}{EC}+\frac{AF}{FB}