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National and Regional Contests
Switzerland Contests
Swiss NMO - geometry
2019.7
2019.7
Part of
Swiss NMO - geometry
Problems
(1)
<ACB = 3 <DCB , if <CAB = 2 <ABC, AD = BD, CD = AC
Source: Switzerland - Swiss ΜΟ 2019 p7
7/14/2020
Let
A
B
C
ABC
A
BC
be a triangle with
∠
C
A
B
=
2
∠
A
B
C
\angle CAB = 2 \angle ABC
∠
C
A
B
=
2∠
A
BC
. Assume that a point
D
D
D
is inside the triangle
A
B
C
ABC
A
BC
exists such that
A
D
=
B
D
AD = BD
A
D
=
B
D
and
C
D
=
A
C
CD = AC
C
D
=
A
C
. Show that
∠
A
C
B
=
3
∠
D
C
B
\angle ACB = 3 \angle DCB
∠
A
CB
=
3∠
D
CB
.
geometry
equal angles
equal segments
angles