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Problem
Problem
An equilateral triangle
P
Q
R
PQR
P
QR
is circumscribed about a given
Δ
A
B
C
\Delta ABC
Δ
A
B
C
. Prove that the maximum area of
Δ
P
Q
R
\Delta PQR
Δ
P
QR
is
2
Δ
+
a
2
+
b
2
+
c
2
2
3
2\Delta + \frac{a^2 + b^2 + c^2}{2\sqrt{3}}
2Δ
+
2
3
a
2
+
b
2
+
c
2
. Where
a
,
b
,
c
a, b, c
a
,
b
,
c
are the sides of
Δ
A
B
C
\Delta ABC
Δ
A
B
C
and
Δ
\Delta
Δ
is its area.
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