MathDB
Problems
Contests
National and Regional Contests
Thailand Contests
Thailand Online MO
2023 Thailand Online MO
4
4
Part of
2023 Thailand Online MO
Problems
(1)
Time to length bash
Source: 2023 Thailand Online MO P4
2/12/2023
Let
A
B
C
ABC
A
BC
be a triangle, and let
D
D
D
and
D
1
D_1
D
1
be points on segment
B
C
BC
BC
such that
B
D
=
C
D
1
BD = CD_1
B
D
=
C
D
1
. Construct point
E
E
E
such that
E
C
⊥
B
C
EC\perp BC
EC
⊥
BC
and
E
D
⊥
A
C
ED\perp AC
E
D
⊥
A
C
. Similarly, construct point
F
F
F
such that
F
B
⊥
B
C
FB\perp BC
FB
⊥
BC
and
F
D
⊥
A
B
FD\perp AB
F
D
⊥
A
B
. Prove that
E
F
⊥
A
D
1
EF\perp AD_1
EF
⊥
A
D
1
.
geometry