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similar triangles around a right triangle

Source: Mexican Mathematical Olympiad 1990 OMM P6

July 29, 2018

geometrysimilar trianglesright triangle

Problem Statement

ABC

is a triangle with

\angle C = 90^o

.

E

is a point on

AC

, and

F

is the midpoint of

EC

.

CH

is an altitude.

I

is the circumcenter of

AHE

, and

G

is the midpoint of

BC

. Show that

ABC

and

IGF

are similar.

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