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National and Regional Contests
Netherlands Contests
Dutch Mathematical Olympiad
1972 Dutch Mathematical Olympiad
5
5
Part of
1972 Dutch Mathematical Olympiad
Problems
(1)
AP/BP in terms of angles of ABC
Source: Netherlands - Dutch NMO 1972 p5
1/27/2023
Given is an acute-angled triangle
A
B
C
ABC
A
BC
with angles
α
\alpha
α
,
β
\beta
β
and
γ
\gamma
γ
. On side
A
B
AB
A
B
lies a point
P
P
P
such that the line connecting the feet of the perpendiculars from
P
P
P
on
A
C
AC
A
C
and
B
C
BC
BC
is parallel to
A
B
AB
A
B
. Express the ratio
A
P
B
P
\frac{AP}{BP}
BP
A
P
in terms of
α
\alpha
α
and
β
\beta
β
.
geometry
ratio