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incenter lies on P_1T_1, <ABC=60^o, PI //BC, TI //AB, AP_1 = B , CT_1 = BT

Source: 2019 Ukraine TST 1.1

November 17, 2020

geometryincenterparallelequal segmentscollinear

Problem Statement

In a triangle

ABC

\angle ABC= 60^o

, point

I

is the incenter. Let the points

P

and

T

on the sides

AB

and

BC

respectively such that

PI \parallel BC

and

TI \parallel AB

, and points

P_1

and

T_1

on the sides

AB

and

BC

respectively such that

AP_1 = BP

and

CT_1 = BT

. Prove that point

I

lies on segment

P_1T_1

.
(Anton Trygub)