MathDB
Problems
Contests
National and Regional Contests
Spain Contests
pOMA and PErA mathematical olympiads
2024 pOMA
4
4
Part of
2024 pOMA
Problems
(1)
Little cute easy geo
Source: pOMA 2024/4
11/14/2024
Let
A
B
C
ABC
A
BC
be a triangle, and let
D
D
D
and
E
E
E
be two points on side
B
C
BC
BC
such that
B
D
=
E
C
BD = EC
B
D
=
EC
. Let
X
X
X
be a point on segment
A
D
AD
A
D
such that
C
X
CX
CX
is parallel to the bisector of
∠
A
D
B
\angle ADB
∠
A
D
B
. Similarly, let
Y
Y
Y
be a point on segment
A
D
AD
A
D
such that
B
Y
BY
B
Y
is parallel to the bisector of
∠
A
D
C
\angle ADC
∠
A
D
C
. Prove that
D
E
=
X
Y
DE = XY
D
E
=
X
Y
.
geometry