Calculate the intersection of a line segment on the radius of a circle
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Given the length and one endpoint of the line segment, how can we find the other endpoint so that it is on the radius of a circle (known coordinates and radius)?
Assume that there is at least one solution.
All variables on the diagram are known except x and y.
geometry circle intersection-theory
edited Dec 23 '18 at 18:34
Larry
2,43331130
asked Dec 23 '18 at 17:47
NathanNathan
34
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add a comment |
$begingroup$
Given the length and one endpoint of the line segment, how can we find the other endpoint so that it is on the radius of a circle (known coordinates and radius)?
Assume that there is at least one solution.
All variables on the diagram are known except x and y.
geometry circle intersection-theory
edited Dec 23 '18 at 18:34
Larry
2,43331130
asked Dec 23 '18 at 17:47
NathanNathan
34
$endgroup$
$begingroup$
will you please make your question a bit more clear by giving a related figure or graph that you want the answer be like?
$endgroup$
– Rakibul Islam Prince
Dec 23 '18 at 18:11
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@RakibulIslamPrince edited
$endgroup$
– Nathan
Dec 23 '18 at 18:31
$begingroup$
Possible duplicate: How can I find the points at which two circles intersect?
$endgroup$
– hardmath
Dec 23 '18 at 18:51
add a comment |
$begingroup$
Given the length and one endpoint of the line segment, how can we find the other endpoint so that it is on the radius of a circle (known coordinates and radius)?
Assume that there is at least one solution.
All variables on the diagram are known except x and y.
geometry circle intersection-theory
edited Dec 23 '18 at 18:34
Larry
2,43331130
asked Dec 23 '18 at 17:47
NathanNathan
34
$endgroup$
Given the length and one endpoint of the line segment, how can we find the other endpoint so that it is on the radius of a circle (known coordinates and radius)?
Assume that there is at least one solution.
All variables on the diagram are known except x and y.
geometry circle intersection-theory
geometry circle intersection-theory
edited Dec 23 '18 at 18:34
Larry
2,43331130
asked Dec 23 '18 at 17:47
NathanNathan
34
edited Dec 23 '18 at 18:34
Larry
2,43331130
asked Dec 23 '18 at 17:47
NathanNathan
34
edited Dec 23 '18 at 18:34
Larry
2,43331130
edited Dec 23 '18 at 18:34
Larry
2,43331130
edited Dec 23 '18 at 18:34
Larry
2,43331130
2,43331130
asked Dec 23 '18 at 17:47
NathanNathan
34
asked Dec 23 '18 at 17:47
NathanNathan
34
asked Dec 23 '18 at 17:47
NathanNathan
34
34
$begingroup$
will you please make your question a bit more clear by giving a related figure or graph that you want the answer be like?
$endgroup$
– Rakibul Islam Prince
Dec 23 '18 at 18:11
$begingroup$
@RakibulIslamPrince edited
$endgroup$
– Nathan
Dec 23 '18 at 18:31
$begingroup$
Possible duplicate: How can I find the points at which two circles intersect?
$endgroup$
– hardmath
Dec 23 '18 at 18:51
add a comment |
$begingroup$
will you please make your question a bit more clear by giving a related figure or graph that you want the answer be like?
$endgroup$
– Rakibul Islam Prince
Dec 23 '18 at 18:11
$begingroup$
@RakibulIslamPrince edited
$endgroup$
– Nathan
Dec 23 '18 at 18:31
$begingroup$
Possible duplicate: How can I find the points at which two circles intersect?
$endgroup$
– hardmath
Dec 23 '18 at 18:51
$begingroup$
will you please make your question a bit more clear by giving a related figure or graph that you want the answer be like?
$endgroup$
– Rakibul Islam Prince
Dec 23 '18 at 18:11
$begingroup$
will you please make your question a bit more clear by giving a related figure or graph that you want the answer be like?
$endgroup$
– Rakibul Islam Prince
Dec 23 '18 at 18:11
$begingroup$
@RakibulIslamPrince edited
$endgroup$
– Nathan
Dec 23 '18 at 18:31
$begingroup$
@RakibulIslamPrince edited
$endgroup$
– Nathan
Dec 23 '18 at 18:31
$begingroup$
Possible duplicate: How can I find the points at which two circles intersect?
$endgroup$
– hardmath
Dec 23 '18 at 18:51
$begingroup$
Possible duplicate: How can I find the points at which two circles intersect?
$endgroup$
– hardmath
Dec 23 '18 at 18:51
add a comment |
1 Answer
1
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oldest
votes
$begingroup$
If $d$ is suitable (you said assume there's a solution), the solutions will come from finding the intersection of the two circles
$$(x-h)^2+(y-k)^2=r^2 qquadtext{and}qquad (x-a)^2+(y-b)^2=d^2.$$
This turns into solving one quadratic and one linear equation. You'll have a unique solution when $d=sqrt{(h-a)^2+(k-b)^2}pm r$, two solutions if $d$ is between those numbers, and no solutions otherwise.
answered Dec 23 '18 at 18:38
Ted ShifrinTed Shifrin
64.2k44692
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add a comment |
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1 Answer
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active
oldest
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1 Answer
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active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
If $d$ is suitable (you said assume there's a solution), the solutions will come from finding the intersection of the two circles
$$(x-h)^2+(y-k)^2=r^2 qquadtext{and}qquad (x-a)^2+(y-b)^2=d^2.$$
This turns into solving one quadratic and one linear equation. You'll have a unique solution when $d=sqrt{(h-a)^2+(k-b)^2}pm r$, two solutions if $d$ is between those numbers, and no solutions otherwise.
answered Dec 23 '18 at 18:38
Ted ShifrinTed Shifrin
64.2k44692
$endgroup$
add a comment |
$begingroup$
If $d$ is suitable (you said assume there's a solution), the solutions will come from finding the intersection of the two circles
$$(x-h)^2+(y-k)^2=r^2 qquadtext{and}qquad (x-a)^2+(y-b)^2=d^2.$$
This turns into solving one quadratic and one linear equation. You'll have a unique solution when $d=sqrt{(h-a)^2+(k-b)^2}pm r$, two solutions if $d$ is between those numbers, and no solutions otherwise.
answered Dec 23 '18 at 18:38
Ted ShifrinTed Shifrin
64.2k44692
$endgroup$
add a comment |
$begingroup$
If $d$ is suitable (you said assume there's a solution), the solutions will come from finding the intersection of the two circles
$$(x-h)^2+(y-k)^2=r^2 qquadtext{and}qquad (x-a)^2+(y-b)^2=d^2.$$
This turns into solving one quadratic and one linear equation. You'll have a unique solution when $d=sqrt{(h-a)^2+(k-b)^2}pm r$, two solutions if $d$ is between those numbers, and no solutions otherwise.
answered Dec 23 '18 at 18:38
Ted ShifrinTed Shifrin
64.2k44692
$endgroup$
If $d$ is suitable (you said assume there's a solution), the solutions will come from finding the intersection of the two circles
$$(x-h)^2+(y-k)^2=r^2 qquadtext{and}qquad (x-a)^2+(y-b)^2=d^2.$$
This turns into solving one quadratic and one linear equation. You'll have a unique solution when $d=sqrt{(h-a)^2+(k-b)^2}pm r$, two solutions if $d$ is between those numbers, and no solutions otherwise.
answered Dec 23 '18 at 18:38
Ted ShifrinTed Shifrin
64.2k44692
answered Dec 23 '18 at 18:38
Ted ShifrinTed Shifrin
64.2k44692
answered Dec 23 '18 at 18:38
Ted ShifrinTed Shifrin
64.2k44692
answered Dec 23 '18 at 18:38
Ted ShifrinTed Shifrin
64.2k44692
64.2k44692
add a comment |
add a comment |
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$begingroup$
will you please make your question a bit more clear by giving a related figure or graph that you want the answer be like?
$endgroup$
– Rakibul Islam Prince
Dec 23 '18 at 18:11
$begingroup$
@RakibulIslamPrince edited
$endgroup$
– Nathan
Dec 23 '18 at 18:31
$begingroup$
Possible duplicate: How can I find the points at which two circles intersect?
$endgroup$
– hardmath
Dec 23 '18 at 18:51