MathDB

C-B=60 <degrees>

Source: Moldova TST 2005, IMO Shortlist 2004 geometry problem 3

April 10, 2005

geometrycircumcirclehomothetyTriangleIMO Shortlist

Problem Statement

Let

O

be the circumcenter of an acute-angled triangle

ABC

with

{\angle B<\angle C}

. The line

AO

meets the side

BC

at

D

. The circumcenters of the triangles

ABD

and

ACD

are

E

and

F

, respectively. Extend the sides

BA

and

CA

beyond

A

, and choose on the respective extensions points

G

and

H

such that

{AG=AC}

and

{AH=AB}

. Prove that the quadrilateral

EFGH

is a rectangle if and only if

{\angle ACB-\angle ABC=60^{\circ }}

.
Proposed by Hojoo Lee, Korea

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