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National and Regional Contests
South Africa Contests
South Africa National Olympiad
2000 South africa National Olympiad
4
4
Part of
2000 South africa National Olympiad
Problems
(1)
Square and perimeter of triangle
Source: South Africa 2000
9/30/2005
A
B
C
D
ABCD
A
BC
D
is a square of side 1.
P
P
P
and
Q
Q
Q
are points on
A
B
AB
A
B
and
B
C
BC
BC
such that
P
D
Q
^
=
4
5
∘
\widehat{PDQ} = 45^{\circ}
P
D
Q
=
4
5
∘
. Find the perimeter of
Δ
P
B
Q
\Delta PBQ
Δ
PBQ
.
geometry
perimeter
trigonometry
function
inequalities
analytic geometry
angle bisector