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International Contests
Tournament Of Towns
1988 Tournament Of Towns
(195) 2
(195) 2
Part of
1988 Tournament Of Towns
Problems
(1)
TOT 195 1988 Autumn Train S2 three equal circumcircles of triangles
Source:
3/7/2021
Let
N
N
N
be the orthocentre of triangle
A
B
C
ABC
A
BC
(i .e. the point where the altitudes meet). Prove that the circumscribed circles of triangles
A
B
N
,
A
C
N
ABN, ACN
A
BN
,
A
CN
and
B
C
N
BCN
BCN
each have equal radius.
geometry
circumcircle
circumradius
orthocenter