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Prove another similarity!

Source: INMO 1994 Problem 1

October 6, 2005

geometryparallelogramratiogeometry solved

Problem Statement

Let

G

be the centroid of the triangle

ABC

in which the angle at

C

is obtuse and

AD

and

\ F

be the medians from

A

and

C

respectively onto the sides

BC

and

AB

. If the points

\ B,\ D, \ G

and

\ F

are concyclic, show that

\dfrac{AC}{BC} \geq \sqrt{2}

. If further

P

is a point on the line

BG

extended such that

AGCP

is a parallelogram, show that triangle

ABC

and

GAP

are similar.

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