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1998 Polish MO Finals
2
Triangle and basic properties
Triangle and basic properties
Source:
November 11, 2005
trigonometry
geometry
trig identities
Law of Sines
geometry solved
Problem Statement
The points
D
,
E
D, E
D
,
E
on the side
A
B
AB
A
B
of the triangle
A
B
C
ABC
A
BC
are such that
A
D
D
B
A
E
E
B
=
(
A
C
C
B
)
2
\frac{AD}{DB}\frac{AE}{EB} = \left(\frac{AC}{CB}\right)^2
D
B
A
D
EB
A
E
=
(
CB
A
C
)
2
. Show that
∠
A
C
D
=
∠
B
C
E
\angle ACD = \angle BCE
∠
A
C
D
=
∠
BCE
.
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