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Old Kyiv MO Geometry
Kyiv City MO Seniors 2003+ geometry
2003.10.4
2003.10.4
Part of
Kyiv City MO Seniors 2003+ geometry
Problems
(1)
angle bisector wanted, 2 right angles (Kyiv City Olympiad 2003 10.4)
Source:
6/27/2021
Let
A
B
C
D
ABCD
A
BC
D
be a convex quadrilateral. The bisector of the angle
A
C
D
ACD
A
C
D
intersects
B
D
BD
B
D
at point
E
E
E
. It is known that
∠
C
A
D
=
∠
B
C
E
=
9
0
o
\angle CAD = \angle BCE= 90^o
∠
C
A
D
=
∠
BCE
=
9
0
o
. Prove that the
A
C
AC
A
C
is the bisector of the angle
B
A
E
BAE
B
A
E
.(Nikolay Nikolay)
geometry
angle bisector