MathDB

concurrency wanted, starting with a 45-135/2 - 135/2 triangle

Source: 2020 Balkan MO shortlist G5

September 14, 2021

geometrycircumcircle

Problem Statement

Let

ABC

be an isosceles triangle with

AB = AC

and

\angle A = 45^o

. Its circumcircle

(c)

has center

O, M

is the midpoint of

F

and

D

is the foot of the perpendicular from

C

to

AB

. With center

C

and radius

CD

we draw a circle which internally intersects

E

at the point

F

and the circle

ZE

at the points

Z

and

E

, such that

Z

lies on the small arc

BC

and

E

on the small arc

AC

. Prove that the lines

ZE

,

CO

,

FM

are concurrent.
Brazitikos Silouanos, Greece

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