The Similar Triangles point.Prove triangles formed by two midpoints and an altitude are congruentTriangle containing most points from a setGeneralization to higher dimensions of a statement about plane trianglesMinimizing the area of the triangles containing a square of side $1$Triangle in perspective to a given triangle but similar to anotherThe total number of non congruent integer sided triangles whose sides belong to the set10,11,12,⋯,22Bisectors of a triangle meet at point.Almost equilateral triangles on latticeFive Similar Triangles from 4-5-6Spherical triangles and congruence criteria
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The Similar Triangles point.
Prove triangles formed by two midpoints and an altitude are congruentTriangle containing most points from a setGeneralization to higher dimensions of a statement about plane trianglesMinimizing the area of the triangles containing a square of side $1$Triangle in perspective to a given triangle but similar to anotherThe total number of non congruent integer sided triangles whose sides belong to the set10,11,12,⋯,22Bisectors of a triangle meet at point.Almost equilateral triangles on latticeFive Similar Triangles from 4-5-6Spherical triangles and congruence criteria
$begingroup$
Any scalene triangle can be dissected into 4 similar but non-congruent triangles in three ways, each with a single pair of congruent triangles. Lines connecting the opposing vertices of these congruent triangles happen to concur at a point.
Which triangle center is this?
The point is at $leftfracx^2+x+y^22 left((x-1) x+y^2+1right),fracy2 left((x-1) x+y^2+1right)right$ for triangle $(0,0), (1,0), (x,y)$.
triangles
asked Feb 21 at 17:22
Ed PeggEd Pegg
10k32593
$endgroup$
add a comment |
$begingroup$
Any scalene triangle can be dissected into 4 similar but non-congruent triangles in three ways, each with a single pair of congruent triangles. Lines connecting the opposing vertices of these congruent triangles happen to concur at a point.
Which triangle center is this?
The point is at $leftfracx^2+x+y^22 left((x-1) x+y^2+1right),fracy2 left((x-1) x+y^2+1right)right$ for triangle $(0,0), (1,0), (x,y)$.
triangles
asked Feb 21 at 17:22
Ed PeggEd Pegg
10k32593
$endgroup$
add a comment |
$begingroup$
Any scalene triangle can be dissected into 4 similar but non-congruent triangles in three ways, each with a single pair of congruent triangles. Lines connecting the opposing vertices of these congruent triangles happen to concur at a point.
Which triangle center is this?
The point is at $leftfracx^2+x+y^22 left((x-1) x+y^2+1right),fracy2 left((x-1) x+y^2+1right)right$ for triangle $(0,0), (1,0), (x,y)$.
triangles
asked Feb 21 at 17:22
Ed PeggEd Pegg
10k32593
$endgroup$
Any scalene triangle can be dissected into 4 similar but non-congruent triangles in three ways, each with a single pair of congruent triangles. Lines connecting the opposing vertices of these congruent triangles happen to concur at a point.
Which triangle center is this?
The point is at $leftfracx^2+x+y^22 left((x-1) x+y^2+1right),fracy2 left((x-1) x+y^2+1right)right$ for triangle $(0,0), (1,0), (x,y)$.
triangles
triangles
asked Feb 21 at 17:22
Ed PeggEd Pegg
10k32593
asked Feb 21 at 17:22
Ed PeggEd Pegg
10k32593
asked Feb 21 at 17:22
Ed PeggEd Pegg
10k32593
asked Feb 21 at 17:22
Ed PeggEd Pegg
10k32593
asked Feb 21 at 17:22
Ed PeggEd Pegg
10k32593
10k32593
add a comment |
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
Turns out it's the symmedian point, X6.
answered Feb 22 at 12:49
Ed PeggEd Pegg
10k32593
$endgroup$
add a comment |
$begingroup$
I have just released a new webpage which makes it much easier to find these centres given a triangle and its cartesian, trilinear or barycentric coordinates:
http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Triangle/tricoords.html
It relies on Clark Kimberling's Encyclopedia for Triangle Centers (ETC) at
http://faculty.evansville.edu/ck6/encyclopedia/ETC.html
It may have a glitch or two so please send comments and corrections to the email address on the page.
answered Mar 29 at 10:04
Ron KnottRon Knott
111
$endgroup$
$begingroup$
These links might give an answer to this question, but it is better to include the essential parts of the answer in the post itself. That way, the answer is always available, even in case the links vanish.
$endgroup$
– Ernie060
Mar 29 at 10:27
add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
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active
oldest
votes
$begingroup$
Turns out it's the symmedian point, X6.
answered Feb 22 at 12:49
Ed PeggEd Pegg
10k32593
$endgroup$
add a comment |
$begingroup$
Turns out it's the symmedian point, X6.
answered Feb 22 at 12:49
Ed PeggEd Pegg
10k32593
$endgroup$
add a comment |
$begingroup$
Turns out it's the symmedian point, X6.
answered Feb 22 at 12:49
Ed PeggEd Pegg
10k32593
$endgroup$
Turns out it's the symmedian point, X6.
answered Feb 22 at 12:49
Ed PeggEd Pegg
10k32593
answered Feb 22 at 12:49
Ed PeggEd Pegg
10k32593
answered Feb 22 at 12:49
Ed PeggEd Pegg
10k32593
answered Feb 22 at 12:49
Ed PeggEd Pegg
10k32593
10k32593
add a comment |
add a comment |
$begingroup$
I have just released a new webpage which makes it much easier to find these centres given a triangle and its cartesian, trilinear or barycentric coordinates:
http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Triangle/tricoords.html
It relies on Clark Kimberling's Encyclopedia for Triangle Centers (ETC) at
http://faculty.evansville.edu/ck6/encyclopedia/ETC.html
It may have a glitch or two so please send comments and corrections to the email address on the page.
answered Mar 29 at 10:04
Ron KnottRon Knott
111
$endgroup$
$begingroup$
These links might give an answer to this question, but it is better to include the essential parts of the answer in the post itself. That way, the answer is always available, even in case the links vanish.
$endgroup$
– Ernie060
Mar 29 at 10:27
add a comment |
$begingroup$
I have just released a new webpage which makes it much easier to find these centres given a triangle and its cartesian, trilinear or barycentric coordinates:
http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Triangle/tricoords.html
It relies on Clark Kimberling's Encyclopedia for Triangle Centers (ETC) at
http://faculty.evansville.edu/ck6/encyclopedia/ETC.html
It may have a glitch or two so please send comments and corrections to the email address on the page.
answered Mar 29 at 10:04
Ron KnottRon Knott
111
$endgroup$
$begingroup$
These links might give an answer to this question, but it is better to include the essential parts of the answer in the post itself. That way, the answer is always available, even in case the links vanish.
$endgroup$
– Ernie060
Mar 29 at 10:27
add a comment |
$begingroup$
I have just released a new webpage which makes it much easier to find these centres given a triangle and its cartesian, trilinear or barycentric coordinates:
http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Triangle/tricoords.html
It relies on Clark Kimberling's Encyclopedia for Triangle Centers (ETC) at
http://faculty.evansville.edu/ck6/encyclopedia/ETC.html
It may have a glitch or two so please send comments and corrections to the email address on the page.
answered Mar 29 at 10:04
Ron KnottRon Knott
111
$endgroup$
I have just released a new webpage which makes it much easier to find these centres given a triangle and its cartesian, trilinear or barycentric coordinates:
http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Triangle/tricoords.html
It relies on Clark Kimberling's Encyclopedia for Triangle Centers (ETC) at
http://faculty.evansville.edu/ck6/encyclopedia/ETC.html
It may have a glitch or two so please send comments and corrections to the email address on the page.
answered Mar 29 at 10:04
Ron KnottRon Knott
111
answered Mar 29 at 10:04
Ron KnottRon Knott
111
answered Mar 29 at 10:04
Ron KnottRon Knott
111
answered Mar 29 at 10:04
Ron KnottRon Knott
111
111
$begingroup$
These links might give an answer to this question, but it is better to include the essential parts of the answer in the post itself. That way, the answer is always available, even in case the links vanish.
$endgroup$
– Ernie060
Mar 29 at 10:27
add a comment |
$begingroup$
These links might give an answer to this question, but it is better to include the essential parts of the answer in the post itself. That way, the answer is always available, even in case the links vanish.
$endgroup$
– Ernie060
Mar 29 at 10:27
$begingroup$
These links might give an answer to this question, but it is better to include the essential parts of the answer in the post itself. That way, the answer is always available, even in case the links vanish.
$endgroup$
– Ernie060
Mar 29 at 10:27
$begingroup$
These links might give an answer to this question, but it is better to include the essential parts of the answer in the post itself. That way, the answer is always available, even in case the links vanish.
$endgroup$
– Ernie060
Mar 29 at 10:27
add a comment |
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