MathDB

Danube Mathematical Competition 2009

Source:

July 15, 2012

Problem Statement

Let be

A

.Let

A'

,

B'

,

C'

be the foot of perpendiculars from

A

,

B

and

C

respectively. The points

E

and

F

are on the sides

CB'

and

BC'

respectively, such that

B'E\cdot C'F = BF\cdot CE

. Show that

AEA'F

is cyclic.

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