MathDB

Geometry

Source: First JBMO TST of France 2020, Problem 2

March 5, 2020

geometry

Problem Statement

Let

ABC

be a triangle and

A

be its circumcircle. Let

P

be the point of intersection of

K_1

with tangent in

A

to

K

. Let

D

and

E

be the symmetrical points of

B

and

A

, respectively, from

P

. Let

K_1

be the circumcircle of triangle

DAC

and let

K_2

the circumscribed circle of triangle

APB

. We denote with

F

the second intersection point of the circles

K_1

and

K_2

Then denote with

G

the second intersection point of the circle

K_1

with

BF

. Show that the lines

BC

and

EG

are parallel.

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