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Sharygin Geometry Olympiad
2010 Sharygin Geometry Olympiad
13
Prove that AK/KC = AD/CD (13)
Prove that AK/KC = AD/CD (13)
Source:
October 29, 2010
geometry unsolved
geometry
Problem Statement
Let us have a convex quadrilateral
A
B
C
D
ABCD
A
BC
D
such that
A
B
=
B
C
.
AB=BC.
A
B
=
BC
.
A point
K
K
K
lies on the diagonal
B
D
,
BD,
B
D
,
and
∠
A
K
B
+
∠
B
K
C
=
∠
A
+
∠
C
.
\angle AKB+\angle BKC=\angle A + \angle C.
∠
A
K
B
+
∠
B
K
C
=
∠
A
+
∠
C
.
Prove that
A
K
⋅
C
D
=
K
C
⋅
A
D
.
AK \cdot CD = KC \cdot AD.
A
K
⋅
C
D
=
K
C
⋅
A
D
.
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