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Danube Competition in Mathematics
2019 Danube Mathematical Competition
4
Inscriptible quadrilateral; angle chasing
Inscriptible quadrilateral; angle chasing
Source: 2019 Danube
October 29, 2019
geometry
cyclic quadrilateral
Problem Statement
Let
A
B
C
D
ABCD
A
BC
D
be a cyclic quadrilateral,
M
M
M
midpoint of
A
C
AC
A
C
and
N
N
N
midpoint of
B
D
.
BD.
B
D
.
If
∠
A
M
B
=
∠
A
M
D
,
\angle AMB =\angle AMD,
∠
A
MB
=
∠
A
M
D
,
prove that
∠
A
N
B
=
∠
B
N
C
.
\angle ANB =\angle BNC.
∠
A
NB
=
∠
BNC
.
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