MathDB

Geometry

Source: Turkey Tst 2017 p3

March 30, 2017

circlesincentergeometry

Problem Statement

At the

ABC

triangle the midpoints of

BC, AC, AB

are respectively

D, E, F

and the triangle tangent to the incircle at

G

,

H

and

I

in the same order.The midpoint of

AD

is

J

.

BJ

and

AG

intersect at point

K

. The

C-

centered circle passing through

A

cuts the

[CB

ray at point

X

. The line passing through

K

and parallel to the

BC

and

AX

meet at

U

.

IU

and

BC

intersect at the

P

point. There is

Y

point chosen at incircle.

PY

is tangent to incircle at point

Y

. Prove that

D, E, F, Y

are cyclic.

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