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2019 Malaysia National Olympiad
B2
Problem B2
Problem B2
Source: 2019 Malaysia OMK
August 21, 2019
geometry
Problem Statement
Given a parallelogram
A
B
C
D
ABCD
A
BC
D
, a point M is chosen such that
∠
D
A
C
=
∠
M
A
C
\angle DAC=\angle MAC
∠
D
A
C
=
∠
M
A
C
and
∠
C
A
B
=
∠
M
A
B
.
\angle CAB=\angle MAB.
∠
C
A
B
=
∠
M
A
B
.
Prove
A
M
B
M
=
(
A
C
B
D
)
2
\frac{AM}{BM}=\left(\frac{AC}{BD}\right)^2
BM
A
M
=
(
B
D
A
C
)
2
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