MathDB

concyclic wanted, starting with right triangle

Source: OLCOMA Costa Rica National Olympiad, Final Round, 2013 3.3

September 25, 2021

geometryright triangleConcyclic

Problem Statement

Let

ABC

be a triangle, right-angled at point

A

and with

AB>AC

. The tangent through

A

of the circumcircle

G

of

ABC

cuts

Y

at

D

.

E

is the reflection of

A

over line

BC

.

X

is the foot of the perpendicular from

A

over

BE

.

Y

is the midpoint of

AX

,

Z

is the intersection of

BY

and

G

other than

B

, and

F

is the intersection of

AE

and

BC

. Prove

D, Z, F, E

are concyclic.

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