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Mathematics
Problem
If
(
x
1
−
x
2
)
2
+
(
y
1
−
y
2
)
2
=
a
2
(x_1 - x_2)^2 + (y_1 - y_2)^2 = a^2
(
x
1
−
x
2
)
2
+
(
y
1
−
y
2
)
2
=
a
2
,
(
x
2
−
x
3
)
2
+
(
y
2
−
y
3
)
2
=
b
2
(x_2 - x_3)^2 + (y_2 - y_3)^2 = b^2
(
x
2
−
x
3
)
2
+
(
y
2
−
y
3
)
2
=
b
2
and
∣
x
1
y
1
1
x
2
y
2
1
x
3
y
3
1
∣
2
=
c
2
\begin{vmatrix} x_1 & y_1 & 1 \\ x_2 & y_2 & 1 \\ x_3 & y_3 & 1 \end{vmatrix}^2 = c^2
x
1
x
2
x
3
y
1
y
2
y
3
1
1
1
2
=
c
2
and
k
=
(
a
+
b
+
c
)
(
b
+
c
−
a
)
(
c
+
a
−
b
)
(
a
+
b
−
c
)
k = (a+b+c)(b+c-a)(c+a-b)(a+b-c)
k
=
(
a
+
b
+
c
)
(
b
+
c
−
a
)
(
c
+
a
−
b
)
(
a
+
b
−
c
)
, the value of
k
k
k
is a. 1 b. 2 c. 4 d. 8
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