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Ukrainian From Tasks to Tasks - geometry
2013.13
2013.13
Part of
Ukrainian From Tasks to Tasks - geometry
Problems
(1)
ABCD, <ABC+<DBC=<ADC+<BDC=180^o (2013 From Tasks to Tasks, p13 Ukr)
Source:
5/2/2021
In the quadrilateral
A
B
C
D
ABCD
A
BC
D
it is known that
A
B
C
+
D
B
C
=
18
0
o
ABC + DBC = 180^o
A
BC
+
D
BC
=
18
0
o
and
A
D
C
+
B
D
C
=
18
0
o
ADC + BDC = 180^o
A
D
C
+
B
D
C
=
18
0
o
. Prove that the center of the circle circumscribed around the triangle
B
C
D
BCD
BC
D
lies on the diagonal
A
C
AC
A
C
.
angles
Circumcenter
geometry