MathDB
Problems
Contests
National and Regional Contests
Russia Contests
Saint Petersburg Mathematical Olympiad
2011 Saint Petersburg Mathematical Olympiad
6
Interesting point
Interesting point
Source: St Petersburg Olympiad 2011, Grade 11, P6
September 15, 2017
geometry
Problem Statement
A
B
C
D
ABCD
A
BC
D
- convex quadrilateral.
M
M
M
-midpoint
A
C
AC
A
C
and
∠
M
C
B
=
∠
C
M
D
=
∠
M
B
A
=
∠
M
B
C
−
∠
M
D
C
\angle MCB=\angle CMD =\angle MBA=\angle MBC-\angle MDC
∠
MCB
=
∠
CM
D
=
∠
MB
A
=
∠
MBC
−
∠
M
D
C
. Prove, that
A
D
=
D
C
+
A
B
AD=DC+AB
A
D
=
D
C
+
A
B
Back to Problems
View on AoPS