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National and Regional Contests
Bulgaria Contests
Bulgaria National Olympiad
1987 Bulgaria National Olympiad
Problem 3
Problem 3
Part of
1987 Bulgaria National Olympiad
Problems
(1)
largest ball in pyramid given side equations
Source: Bulgaria 1987 P3
6/15/2021
Let
M
A
B
C
D
MABCD
M
A
BC
D
be a pyramid with the square
A
B
C
D
ABCD
A
BC
D
as the base, in which
M
A
=
M
D
MA=MD
M
A
=
M
D
,
M
A
2
+
A
B
2
=
M
B
2
MA^2+AB^2=MB^2
M
A
2
+
A
B
2
=
M
B
2
and the area of
△
A
D
M
\triangle ADM
△
A
D
M
is equal to
1
1
1
. Determine the radius of the largest ball that is contained in the given pyramid.
geometry
3D geometry
pyramid