MathDB

isosceles wanted, arc midpoint, circumcircle, perp. bisector related

Source: II Brazilian Olympic Revenge 2003 p1

April 22, 2020

geometrycircumcirclearc midpointperpendicularisosceles

Problem Statement

Let

ABC

be a triangle with circumcircle

\Gamma

D

is the midpoint of arc

BC

(this arc does not contain

A

E

is the common point of

BC

and the perpendicular bisector of

BD

F

is the common point of

AC

and the parallel to

AB

containing

D

G

is the common point of

EF

and

AB

H

is the common point of

GD

and

AC

. Show that

GAH

is isosceles.