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Problem
Problem
Statement I
A
A
1
,
B
B
1
,
C
C
1
AA_1, BB_1, CC_1
A
A
1
,
B
B
1
,
C
C
1
are the medians of triangle
A
B
C
ABC
A
B
C
whose centroid is
G
G
G
. If the points
A
,
C
1
,
G
A, C_1, G
A
,
C
1
,
G
and
B
B
B
are concyclic, then
c
2
,
a
2
,
b
2
c^2, a^2, b^2
c
2
,
a
2
,
b
2
are in AP.
Statement II
B
G
⋅
C
C
1
=
B
C
1
⋅
B
A
BG \cdot CC_1 = BC_1 \cdot BA
B
G
⋅
C
C
1
=
B
C
1
⋅
B
A
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