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Polish MO Finals
1951 Polish MO Finals
6
6
Part of
1951 Polish MO Finals
Problems
(1)
construction of a point, similar triangles
Source: Polish MO Finals 1951 p6
8/28/2024
Given a circle and a segment
M
N
MN
MN
. Find a point
C
C
C
on the circle such that the triangle
A
B
C
ABC
A
BC
, where
A
A
A
and
B
B
B
are the intersection points of the lines
M
C
MC
MC
and
N
C
NC
NC
with the circle, is similar to the triangle
M
N
C
MNC
MNC
.
similar
similar triangles
construction
geometry