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International Contests
Tournament Of Towns
1993 Tournament Of Towns
(358) 1
(358) 1
Part of
1993 Tournament Of Towns
Problems
(1)
TOT 358 1993 Spring O J1 distance between 2 orthocenters
Source:
6/10/2024
Let
M
M
M
be a point on the side
A
B
AB
A
B
of triangle
A
B
C
ABC
A
BC
. The length
A
B
=
c
AB = c
A
B
=
c
and
∠
C
M
A
=
ϕ
\angle CMA=\phi
∠
CM
A
=
ϕ
are given. Find the distance between the orthocentres (intersection points of altitudes) of the triangles
A
M
C
AMC
A
MC
and
B
M
C
BMC
BMC
. (IF Sharygin)
geometry
orthocenter