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Slovenia 2019 TST1 P5

Source: 2019 Slovenia 1st TST Problem 5

February 19, 2019

TSTgeometry

Problem Statement

Let

ABC

be a triangle and

D, E

and

F

the foots of heights from

A, B

and

C

respectively. Let

D_1

be such a point on

EF

, that

DF = D_1 E

where

E

is between

D_1

and

F

. Similarly, let

D_2

be such a point on

EF

, that

DE = D_2 F

where

F

is between

E

and

D_2

. Let the bisector of

DD_1

intersect

AB

at

P

and let the bisector of

DD_2

intersect

AC

at

Q

. Prove that,

PQ

bisects

BC

.

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