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Miklós Schweitzer
1954 Miklós Schweitzer
10
10
Part of
1954 Miklós Schweitzer
Problems
(1)
Miklós Schweitzer 1954- Problem 10
Source:
9/29/2015
10. Given a triangle
A
B
C
ABC
A
BC
, construct outwards over the sides
A
B
,
B
C
,
C
A
AB, BC, CA
A
B
,
BC
,
C
A
similiar isosceles triangles
A
B
C
1
,
B
C
A
1
ABC_{1}, BCA_{1}
A
B
C
1
,
BC
A
1
and
C
A
B
1
CAB_{1}
C
A
B
1
. Prove that the straight lines
A
A
1
.
B
B
1
AA_{1}. BB_{1}
A
A
1
.
B
B
1
and
C
C
1
CC_{1}
C
C
1
are concurrent. Is this statemente true in elliptic and hyperbolic geometry, too? (G. 19)
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