MathDB

Given an acute

\vartriangle ABC

with incenter

I

. Let

I'

be the symmetric point

I

with respect to the midpoint of

B,C

and

D

is the foot of

A

. If

DI

and the circumcircle of vartriangle

BI'C

intersect at

T

and

TI'

intersects the circumcircle of

\vartriangle ATI

X

. Furthermore,

E,F

are tangent points of the incircle and

AB,AC, P

is the another intersection of the circumcircles of

\vartriangle ABC, \vartriangle AEF

. Show that

AX \parallel PI

. https://3.bp.blogspot.com/-tj9A8HIR6Vw/XndLEPMRvnI/AAAAAAAALfk/2vw_pZbhpnkTKIc1BcKf4K7SNZ11vu4TACK4BGAYYCw/s1600/2018%2Bimoc%2Bg4.png

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