Is there an easy way to find the sign of this determinant without calculating it directly?
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There exist real numbers $A_x, A_y, B_x, B_y, C_x, C_y, D_x$ and $D_y$. Is there an easy way to find the sign of following determinant without calculating it directly? BTW, the determinant appears when judging whether or not point $D$ is inside the circumcircle of triangle $ABC$ on the plane.
$$
left|
begin{array}{ccc}
A_x - D_x & A_y - D_y & (A_x - D_x)^2 + (A_y - D_y)^2 \
B_x - D_x & B_y - D_y & (B_x - D_x)^2 + (B_y - D_y)^2 \
C_x - D_x & C_y - D_y & (C_x - D_x)^2 + (C_y - D_y)^2
end{array}
right|
$$
determinant triangle circle triangulation
asked Nov 15 at 18:29
cia_rana
1012
add a comment |
up vote
0
down vote
favorite
There exist real numbers $A_x, A_y, B_x, B_y, C_x, C_y, D_x$ and $D_y$. Is there an easy way to find the sign of following determinant without calculating it directly? BTW, the determinant appears when judging whether or not point $D$ is inside the circumcircle of triangle $ABC$ on the plane.
$$
left|
begin{array}{ccc}
A_x - D_x & A_y - D_y & (A_x - D_x)^2 + (A_y - D_y)^2 \
B_x - D_x & B_y - D_y & (B_x - D_x)^2 + (B_y - D_y)^2 \
C_x - D_x & C_y - D_y & (C_x - D_x)^2 + (C_y - D_y)^2
end{array}
right|
$$
determinant triangle circle triangulation
asked Nov 15 at 18:29
cia_rana
1012
At a glance, this would be way easier to read if the subscripts were removed and every argument was just assigned a single letter.
– The Count
Nov 19 at 4:50
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
There exist real numbers $A_x, A_y, B_x, B_y, C_x, C_y, D_x$ and $D_y$. Is there an easy way to find the sign of following determinant without calculating it directly? BTW, the determinant appears when judging whether or not point $D$ is inside the circumcircle of triangle $ABC$ on the plane.
$$
left|
begin{array}{ccc}
A_x - D_x & A_y - D_y & (A_x - D_x)^2 + (A_y - D_y)^2 \
B_x - D_x & B_y - D_y & (B_x - D_x)^2 + (B_y - D_y)^2 \
C_x - D_x & C_y - D_y & (C_x - D_x)^2 + (C_y - D_y)^2
end{array}
right|
$$
determinant triangle circle triangulation
asked Nov 15 at 18:29
cia_rana
1012
There exist real numbers $A_x, A_y, B_x, B_y, C_x, C_y, D_x$ and $D_y$. Is there an easy way to find the sign of following determinant without calculating it directly? BTW, the determinant appears when judging whether or not point $D$ is inside the circumcircle of triangle $ABC$ on the plane.
$$
left|
begin{array}{ccc}
A_x - D_x & A_y - D_y & (A_x - D_x)^2 + (A_y - D_y)^2 \
B_x - D_x & B_y - D_y & (B_x - D_x)^2 + (B_y - D_y)^2 \
C_x - D_x & C_y - D_y & (C_x - D_x)^2 + (C_y - D_y)^2
end{array}
right|
$$
determinant triangle circle triangulation
determinant triangle circle triangulation
asked Nov 15 at 18:29
cia_rana
1012
asked Nov 15 at 18:29
cia_rana
1012
edited Nov 19 at 4:46
asked Nov 15 at 18:29
cia_rana
1012
asked Nov 15 at 18:29
cia_rana
1012
asked Nov 15 at 18:29
cia_rana
1012
1012
At a glance, this would be way easier to read if the subscripts were removed and every argument was just assigned a single letter.
– The Count
Nov 19 at 4:50
add a comment |
At a glance, this would be way easier to read if the subscripts were removed and every argument was just assigned a single letter.
– The Count
Nov 19 at 4:50
At a glance, this would be way easier to read if the subscripts were removed and every argument was just assigned a single letter.
– The Count
Nov 19 at 4:50
At a glance, this would be way easier to read if the subscripts were removed and every argument was just assigned a single letter.
– The Count
Nov 19 at 4:50
add a comment |
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At a glance, this would be way easier to read if the subscripts were removed and every argument was just assigned a single letter.
– The Count
Nov 19 at 4:50