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Old Kyiv MO Geometry
Kyiv City MO Juniors Round2 2010+ geometry
2020.8.2
2020.8.2
Part of
Kyiv City MO Juniors Round2 2010+ geometry
Problems
(1)
CA =CD wanted, <CBD = 90^o,<BCD =<CAD, AD=2BC (2020 Kyiv City MO Round2 8.2)
Source:
9/21/2020
Given a convex quadrilateral
A
B
C
D
ABCD
A
BC
D
, in which
∠
C
B
D
=
9
0
o
\angle CBD = 90^o
∠
CB
D
=
9
0
o
,
∠
B
C
D
=
∠
C
A
D
\angle BCD =\angle CAD
∠
BC
D
=
∠
C
A
D
and
A
D
=
2
B
C
AD= 2BC
A
D
=
2
BC
. Prove that
C
A
=
C
D
CA =CD
C
A
=
C
D
.(Anton Trygub)
geometry
equal segments
equal angles
right angle