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Parallel Lines with Incenter Properties

Source: 2022 IRN TWN Friendly Math Competition P3

June 21, 2022

geometryincenterTaiwanIranparallelincircle

Problem Statement

Let

ABC

be a scalene triangle with

I

be its incenter. The incircle touches

BC

,

CA

,

AB

at

D

,

E

,

F

, respectively.

Y

,

Z

are the midpoints of

DF

,

DE

respectively, and

S

,

V

are the intersections of lines

YZ

and

BC

,

AD

, respectively.

T

is the second intersection of

\odot(ABC)

and

AS

.

K

is the foot from

I

to

AT

. Prove that

KV

is parallel to

DT

.
Proposed by ltf0501

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