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Contests
National and Regional Contests
Bangladesh Contests
Bangladesh Mathematical Olympiad
2019 Bangladesh Mathematical Olympiad
9
9
Part of
2019 Bangladesh Mathematical Olympiad
Problems
(1)
BdMO National Higher Secondary 2019/9
Source: BdMO National Higher Secondary 2019/9
3/4/2019
Let
A
B
C
D
ABCD
A
BC
D
is a convex quadrilateral.The internal angle bisectors of
∠
B
A
C
\angle {BAC}
∠
B
A
C
and
∠
B
D
C
\angle {BDC}
∠
B
D
C
meets at
P
P
P
.
∠
A
P
B
=
∠
C
P
D
\angle {APB}=\angle {CPD}
∠
A
PB
=
∠
CP
D
.Prove that
A
B
+
B
D
=
A
C
+
C
D
AB+BD=AC+CD
A
B
+
B
D
=
A
C
+
C
D
.
geometry