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ratio of areas AEGH/ABCD in trapezoid ABCD, midpoints

Source: 2004 All-Ukrainian Correspondence MO of magazine ''In the World of Mathematics'', grades 5-11 p8

April 28, 2021

geometryratiotrapezoidareasUkraine Correspondence

Problem Statement

The extensions of the sides

AB

and

CD

of the trapezoid

ABCD

intersect at point

E

. Denote by

H

and

G

the midpoints of

BD

and

AC

. Find the ratio of the area

AEGH

to the area

ABCD