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Silk Road
2010 Silk Road
1
1
Part of
2010 Silk Road
Problems
(1)
convex ABCD, <ADB +<ACB = <CAB + <DBA =30^o, AD=BC, right triangle
Source: SRMC 2010 P1
8/30/2018
In a convex quadrilateral it is known
A
B
C
D
ABCD
A
BC
D
that
∠
A
D
B
+
∠
A
C
B
=
∠
C
A
B
+
∠
D
B
A
=
3
0
∘
\angle ADB + \angle ACB = \angle CAB + \angle DBA = 30^{\circ}
∠
A
D
B
+
∠
A
CB
=
∠
C
A
B
+
∠
D
B
A
=
3
0
∘
and
A
D
=
B
C
AD = BC
A
D
=
BC
. Prove that from the lengths
D
B
DB
D
B
,
C
A
CA
C
A
and
D
C
DC
D
C
, you can make a right triangle.
geometry
convex quadrilateral
angles
right triangle