Mixing
incenter point coordinates given the coordinates of the three vertices of a triangle ABC
$begingroup$
I have the following equations: ,
,
.These equations determine a triangle.I have to find the incenter coordinates.
I found the coordinates of the triangle vertices and all I know is that I take the incenter point then
How to continue?
geometry
asked Jan 10 at 10:23
Vali ROVali RO
736
$endgroup$
add a comment |
$begingroup$
I have the following equations: ,
,
.These equations determine a triangle.I have to find the incenter coordinates.
I found the coordinates of the triangle vertices and all I know is that I take the incenter point then
How to continue?
geometry
asked Jan 10 at 10:23
Vali ROVali RO
736
$endgroup$
$begingroup$
Hint: The internal bisector of the angle at (8, 0) is the x-axis. So b = 0.
$endgroup$
– Michael Behrend
Jan 10 at 12:20
add a comment |
$begingroup$
I have the following equations: ,
,
.These equations determine a triangle.I have to find the incenter coordinates.
I found the coordinates of the triangle vertices and all I know is that I take the incenter point then
How to continue?
geometry
asked Jan 10 at 10:23
Vali ROVali RO
736
$endgroup$
I have the following equations: ,
,
.These equations determine a triangle.I have to find the incenter coordinates.
I found the coordinates of the triangle vertices and all I know is that I take the incenter point then
How to continue?
geometry
geometry
asked Jan 10 at 10:23
Vali ROVali RO
736
asked Jan 10 at 10:23
Vali ROVali RO
736
asked Jan 10 at 10:23
Vali ROVali RO
736
asked Jan 10 at 10:23
Vali ROVali RO
736
asked Jan 10 at 10:23
Vali ROVali RO
736
736
$begingroup$
Hint: The internal bisector of the angle at (8, 0) is the x-axis. So b = 0.
$endgroup$
– Michael Behrend
Jan 10 at 12:20
add a comment |
$begingroup$
Hint: The internal bisector of the angle at (8, 0) is the x-axis. So b = 0.
$endgroup$
– Michael Behrend
Jan 10 at 12:20
$begingroup$
Hint: The internal bisector of the angle at (8, 0) is the x-axis. So b = 0.
$endgroup$
– Michael Behrend
Jan 10 at 12:20
$begingroup$
Hint: The internal bisector of the angle at (8, 0) is the x-axis. So b = 0.
$endgroup$
– Michael Behrend
Jan 10 at 12:20
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Guide:
It is know that for a $triangle ABC$, suppose its length is $a,b,c$, with the vertices being $(x_i, y_i)$ where $iin {A,B,C}$.
Then the formula is given by
$$left( frac{ax_A+bx_B+cx_C}{a+b+c},frac{ay_A+by_B+cy_C}{a+b+c}right)$$
A proof of the formula can be found here.
You have found the coordinates, hence it should be possible for you to find the lenght of the sides easily.
answered Jan 10 at 12:25
Siong Thye GohSiong Thye Goh
101k1466118
$endgroup$
$begingroup$
Thanks a lot!I did it.
$endgroup$
– Vali RO
Jan 10 at 14:25
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Guide:
It is know that for a $triangle ABC$, suppose its length is $a,b,c$, with the vertices being $(x_i, y_i)$ where $iin {A,B,C}$.
Then the formula is given by
$$left( frac{ax_A+bx_B+cx_C}{a+b+c},frac{ay_A+by_B+cy_C}{a+b+c}right)$$
A proof of the formula can be found here.
You have found the coordinates, hence it should be possible for you to find the lenght of the sides easily.
answered Jan 10 at 12:25
Siong Thye GohSiong Thye Goh
101k1466118
$endgroup$
$begingroup$
Thanks a lot!I did it.
$endgroup$
– Vali RO
Jan 10 at 14:25
add a comment |
$begingroup$
Guide:
It is know that for a $triangle ABC$, suppose its length is $a,b,c$, with the vertices being $(x_i, y_i)$ where $iin {A,B,C}$.
Then the formula is given by
$$left( frac{ax_A+bx_B+cx_C}{a+b+c},frac{ay_A+by_B+cy_C}{a+b+c}right)$$
A proof of the formula can be found here.
You have found the coordinates, hence it should be possible for you to find the lenght of the sides easily.
answered Jan 10 at 12:25
Siong Thye GohSiong Thye Goh
101k1466118
$endgroup$
$begingroup$
Thanks a lot!I did it.
$endgroup$
– Vali RO
Jan 10 at 14:25
add a comment |
$begingroup$
Guide:
It is know that for a $triangle ABC$, suppose its length is $a,b,c$, with the vertices being $(x_i, y_i)$ where $iin {A,B,C}$.
Then the formula is given by
$$left( frac{ax_A+bx_B+cx_C}{a+b+c},frac{ay_A+by_B+cy_C}{a+b+c}right)$$
A proof of the formula can be found here.
You have found the coordinates, hence it should be possible for you to find the lenght of the sides easily.
answered Jan 10 at 12:25
Siong Thye GohSiong Thye Goh
101k1466118
$endgroup$
Guide:
It is know that for a $triangle ABC$, suppose its length is $a,b,c$, with the vertices being $(x_i, y_i)$ where $iin {A,B,C}$.
Then the formula is given by
$$left( frac{ax_A+bx_B+cx_C}{a+b+c},frac{ay_A+by_B+cy_C}{a+b+c}right)$$
A proof of the formula can be found here.
You have found the coordinates, hence it should be possible for you to find the lenght of the sides easily.
answered Jan 10 at 12:25
Siong Thye GohSiong Thye Goh
101k1466118
answered Jan 10 at 12:25
Siong Thye GohSiong Thye Goh
101k1466118
answered Jan 10 at 12:25
Siong Thye GohSiong Thye Goh
101k1466118
answered Jan 10 at 12:25
Siong Thye GohSiong Thye Goh
101k1466118
101k1466118
$begingroup$
Thanks a lot!I did it.
$endgroup$
– Vali RO
Jan 10 at 14:25
add a comment |
$begingroup$
Thanks a lot!I did it.
$endgroup$
– Vali RO
Jan 10 at 14:25
$begingroup$
Thanks a lot!I did it.
$endgroup$
– Vali RO
Jan 10 at 14:25
$begingroup$
Thanks a lot!I did it.
$endgroup$
– Vali RO
Jan 10 at 14:25
add a comment |
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$begingroup$
Hint: The internal bisector of the angle at (8, 0) is the x-axis. So b = 0.
$endgroup$
– Michael Behrend
Jan 10 at 12:20