MathDB

Cute intersection of the bisector and side

Source: Turkey National Mathematical Olympiad 2021 P4

January 6, 2022

geometrygeometry proposedangle bisectorZ -orthocenter

Problem Statement

Points

D

and

E

are taken on

[BC]

and

[AC]

of acute angled triangle

ABC

such that

BD

and

CE

are angle bisectors. Projections of

D

onto

BC

and

BA

are

P

and

Q

, projections of

E

onto

CA

and

CB

are

R

and

S

. Let

AP \cap CQ=X

AS \cap BR=Y

and

BX \cap CY=Z

. Show that

AZ \perp BC