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Baltic Way
2014 Baltic Way
13
13
Part of
2014 Baltic Way
Problems
(1)
Triangles with equal areas
Source: Baltic Way 2014, Problem 13
11/11/2014
Let
A
B
C
D
ABCD
A
BC
D
be a square inscribed in a circle
ω
\omega
ω
and let
P
P
P
be a point on the shorter arc
A
B
AB
A
B
of
ω
\omega
ω
. Let
C
P
∩
B
D
=
R
CP\cap BD = R
CP
∩
B
D
=
R
and
D
P
∩
A
C
=
S
.
DP \cap AC = S.
D
P
∩
A
C
=
S
.
Show that triangles
A
R
B
ARB
A
RB
and
D
S
R
DSR
D
SR
have equal areas.
geometry
trigonometry
circumcircle
trig identities
Law of Sines
geometry proposed