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Contests
National and Regional Contests
Serbia Contests
Serbia Team Selection Test
1995 Yugoslav Team Selection Test
Problem 3
Problem 3
Part of
1995 Yugoslav Team Selection Test
Problems
(1)
find pyramid side ratios
Source: Yugoslav TST 1995 P3
5/27/2021
Let
S
A
B
C
D
SABCD
S
A
BC
D
be a pyramid with the vertex
S
S
S
whose all edges are equal. Points
M
M
M
and
N
N
N
on the edges
S
A
SA
S
A
and
B
C
BC
BC
respectively are such that
M
N
MN
MN
is perpendicular to both
S
A
SA
S
A
and
B
C
BC
BC
. Find the ratios
S
M
:
M
A
SM:MA
SM
:
M
A
and
B
N
:
N
C
BN:NC
BN
:
NC
.
geometry
3D geometry
pyramid
ratio