MathDB
Problems
Contests
National and Regional Contests
China Contests
China Northern MO
2017 China Northern MO
3
3
Part of
2017 China Northern MO
Problems
(1)
China Northern Mathematical Olympiad 2017, Problem 3
Source: China Northern Mathematical Olympiad 2017
7/29/2017
Let
D
D
D
be the midpoint of side
B
C
BC
BC
of triangle
A
B
C
ABC
A
BC
. Let
E
,
F
E, F
E
,
F
be points on sides
A
B
,
A
C
AB, AC
A
B
,
A
C
respectively such that
D
E
=
D
F
DE = DF
D
E
=
D
F
. Prove that
A
E
+
A
F
=
B
E
+
C
F
⟺
∠
E
D
F
=
∠
B
A
C
AE + AF = BE + CF \iff \angle EDF = \angle BAC
A
E
+
A
F
=
BE
+
CF
⟺
∠
E
D
F
=
∠
B
A
C
.
geometry
Spiral Similarity
Triangle