MathDB
Problems
Contests
International Contests
Middle European Mathematical Olympiad
2023 Middle European Mathematical Olympiad
3
Easy incircle geo
Easy incircle geo
Source: MEMO 2023 I3
August 24, 2023
geometry
MEMO2023
Problem Statement
Let
A
B
C
ABC
A
BC
be a triangle with incenter
I
I
I
, and the incircle touches
B
C
BC
BC
at
D
D
D
. The points
E
,
F
E, F
E
,
F
are such that
B
E
∥
A
I
∥
C
F
BE \parallel AI \parallel CF
BE
∥
A
I
∥
CF
and
∠
B
E
I
=
∠
C
F
I
=
9
0
∘
\angle BEI=\angle CFI=90^{\circ}
∠
BE
I
=
∠
CF
I
=
9
0
∘
. If
D
E
,
D
F
DE, DF
D
E
,
D
F
meet the incircle at
E
′
,
F
′
E', F'
E
′
,
F
′
, show that
E
′
F
′
⊥
A
I
E'F' \perp AI
E
′
F
′
⊥
A
I
.
Back to Problems
View on AoPS