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National and Regional Contests
Mexico Contests
Mexico National Olympiad
1987 Mexico National Olympiad
3
3
Part of
1987 Mexico National Olympiad
Problems
(1)
locus of projection so that a triangle is right
Source: 1st Mexican Mathematical Olympiad 1987 OMM P3
7/27/2018
Consider two lines
ℓ
\ell
ℓ
and
ℓ
′
\ell '
ℓ
′
and a fixed point
P
P
P
equidistant from these lines. What is the locus of projections
M
M
M
of
P
P
P
on
A
B
AB
A
B
, where
A
A
A
is on
ℓ
\ell
ℓ
,
B
B
B
on
ℓ
′
\ell '
ℓ
′
, and angle
∠
A
P
B
\angle APB
∠
A
PB
is right?
geometry
Locus
projections