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Compass and straight-edge construction of a line
The Next CEO of Stack OverflowDynamic Geometry Software for Straight-edge and Compass ConstructionsCircles intersecting at A and B3D Dodecahedron model: Construction question.Find the length of a tangent line of a circleMoving Line Segment ProblemGeometry experts! Three equal tangential circles: What is the ratio of the blue line to the red line?What is the minimum radius $r$ of two intersecting circles that are spaced $x$ apart that completely enclose a square of length $w$?Construction of tangent circlesIs the small circle the straight line on the sphere?Find the angle of a tangent line between two circles
$begingroup$
How to construct a line of given length L whose two ends lie on two fixed circles of radii b and c and centers of the circles being at a distance a from each other? Two different cases of construction required.
1. The required line is parallel to the line joining the centers.
2. The required line makes an angle $theta$ with the line joining the centers.
Assuming such a line exists in each case. Am trying to attach this diagram. But the description is complete without it.
https://www.geogebra.or/upload/5c9b620b11fd4
geometry
asked yesterday
Anirban Anirban
132
New contributor
Anirban is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
How to construct a line of given length L whose two ends lie on two fixed circles of radii b and c and centers of the circles being at a distance a from each other? Two different cases of construction required.
1. The required line is parallel to the line joining the centers.
2. The required line makes an angle $theta$ with the line joining the centers.
Assuming such a line exists in each case. Am trying to attach this diagram. But the description is complete without it.
https://www.geogebra.or/upload/5c9b620b11fd4
geometry
asked yesterday
Anirban Anirban
132
New contributor
Anirban is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
$begingroup$
The page is not accessible.
$endgroup$
– Yves Daoust
yesterday
$begingroup$
Hi Yves, sorry - I am new to this site. Haven't yet learnt how to upload a picture. I bungled it this time. I hope to learn it quickly.
$endgroup$
– Anirban
yesterday
add a comment |
$begingroup$
How to construct a line of given length L whose two ends lie on two fixed circles of radii b and c and centers of the circles being at a distance a from each other? Two different cases of construction required.
1. The required line is parallel to the line joining the centers.
2. The required line makes an angle $theta$ with the line joining the centers.
Assuming such a line exists in each case. Am trying to attach this diagram. But the description is complete without it.
https://www.geogebra.or/upload/5c9b620b11fd4
geometry
asked yesterday
Anirban Anirban
132
New contributor
Anirban is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
How to construct a line of given length L whose two ends lie on two fixed circles of radii b and c and centers of the circles being at a distance a from each other? Two different cases of construction required.
1. The required line is parallel to the line joining the centers.
2. The required line makes an angle $theta$ with the line joining the centers.
Assuming such a line exists in each case. Am trying to attach this diagram. But the description is complete without it.
https://www.geogebra.or/upload/5c9b620b11fd4
geometry
geometry
asked yesterday
Anirban Anirban
132
New contributor
Anirban is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked yesterday
Anirban Anirban
132
New contributor
Anirban is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked yesterday
Anirban Anirban
132
New contributor
Anirban is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked yesterday
Anirban Anirban
132
asked yesterday
Anirban Anirban
132
132
New contributor
Anirban is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Anirban is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Anirban is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$begingroup$
The page is not accessible.
$endgroup$
– Yves Daoust
yesterday
$begingroup$
Hi Yves, sorry - I am new to this site. Haven't yet learnt how to upload a picture. I bungled it this time. I hope to learn it quickly.
$endgroup$
– Anirban
yesterday
add a comment |
$begingroup$
The page is not accessible.
$endgroup$
– Yves Daoust
yesterday
$begingroup$
Hi Yves, sorry - I am new to this site. Haven't yet learnt how to upload a picture. I bungled it this time. I hope to learn it quickly.
$endgroup$
– Anirban
yesterday
$begingroup$
The page is not accessible.
$endgroup$
– Yves Daoust
yesterday
$begingroup$
The page is not accessible.
$endgroup$
– Yves Daoust
yesterday
$begingroup$
Hi Yves, sorry - I am new to this site. Haven't yet learnt how to upload a picture. I bungled it this time. I hope to learn it quickly.
$endgroup$
– Anirban
yesterday
$begingroup$
Hi Yves, sorry - I am new to this site. Haven't yet learnt how to upload a picture. I bungled it this time. I hope to learn it quickly.
$endgroup$
– Anirban
yesterday
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
First problem:
Draw a line joining the centers. Suppose it intersects circles at points A and B respectively.
Do a bisection of A and B, let it be point C.
Put points D and E on AB (opposite sides of C), such that DC=L/2 and EC=L/2.
Draw lines orthogonal to AB through points D and E. Suppose that these lines intersect circles at F and G.
Connect F and G - you've got the answer.
All this assuming that solution exists.
answered yesterday
AlexAlex
233
$endgroup$
$begingroup$
Hi Alex, looks to me that your solution would work if the circles are of same radius. But if they are of different radius, then FG is not parallel to the line joining the centers and also does not have a length L. Correct me if I am wrong.
$endgroup$
– Anirban
yesterday
add a comment |
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1 Answer
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active
oldest
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1 Answer
1
active
oldest
votes
active
oldest
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active
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votes
$begingroup$
First problem:
Draw a line joining the centers. Suppose it intersects circles at points A and B respectively.
Do a bisection of A and B, let it be point C.
Put points D and E on AB (opposite sides of C), such that DC=L/2 and EC=L/2.
Draw lines orthogonal to AB through points D and E. Suppose that these lines intersect circles at F and G.
Connect F and G - you've got the answer.
All this assuming that solution exists.
answered yesterday
AlexAlex
233
$endgroup$
$begingroup$
Hi Alex, looks to me that your solution would work if the circles are of same radius. But if they are of different radius, then FG is not parallel to the line joining the centers and also does not have a length L. Correct me if I am wrong.
$endgroup$
– Anirban
yesterday
add a comment |
$begingroup$
First problem:
Draw a line joining the centers. Suppose it intersects circles at points A and B respectively.
Do a bisection of A and B, let it be point C.
Put points D and E on AB (opposite sides of C), such that DC=L/2 and EC=L/2.
Draw lines orthogonal to AB through points D and E. Suppose that these lines intersect circles at F and G.
Connect F and G - you've got the answer.
All this assuming that solution exists.
answered yesterday
AlexAlex
233
$endgroup$
$begingroup$
Hi Alex, looks to me that your solution would work if the circles are of same radius. But if they are of different radius, then FG is not parallel to the line joining the centers and also does not have a length L. Correct me if I am wrong.
$endgroup$
– Anirban
yesterday
add a comment |
$begingroup$
First problem:
Draw a line joining the centers. Suppose it intersects circles at points A and B respectively.
Do a bisection of A and B, let it be point C.
Put points D and E on AB (opposite sides of C), such that DC=L/2 and EC=L/2.
Draw lines orthogonal to AB through points D and E. Suppose that these lines intersect circles at F and G.
Connect F and G - you've got the answer.
All this assuming that solution exists.
answered yesterday
AlexAlex
233
$endgroup$
First problem:
Draw a line joining the centers. Suppose it intersects circles at points A and B respectively.
Do a bisection of A and B, let it be point C.
Put points D and E on AB (opposite sides of C), such that DC=L/2 and EC=L/2.
Draw lines orthogonal to AB through points D and E. Suppose that these lines intersect circles at F and G.
Connect F and G - you've got the answer.
All this assuming that solution exists.
answered yesterday
AlexAlex
233
answered yesterday
AlexAlex
233
answered yesterday
AlexAlex
233
answered yesterday
AlexAlex
233
233
$begingroup$
Hi Alex, looks to me that your solution would work if the circles are of same radius. But if they are of different radius, then FG is not parallel to the line joining the centers and also does not have a length L. Correct me if I am wrong.
$endgroup$
– Anirban
yesterday
add a comment |
$begingroup$
Hi Alex, looks to me that your solution would work if the circles are of same radius. But if they are of different radius, then FG is not parallel to the line joining the centers and also does not have a length L. Correct me if I am wrong.
$endgroup$
– Anirban
yesterday
$begingroup$
Hi Alex, looks to me that your solution would work if the circles are of same radius. But if they are of different radius, then FG is not parallel to the line joining the centers and also does not have a length L. Correct me if I am wrong.
$endgroup$
– Anirban
yesterday
$begingroup$
Hi Alex, looks to me that your solution would work if the circles are of same radius. But if they are of different radius, then FG is not parallel to the line joining the centers and also does not have a length L. Correct me if I am wrong.
$endgroup$
– Anirban
yesterday
add a comment |
Anirban is a new contributor. Be nice, and check out our Code of Conduct.
Anirban is a new contributor. Be nice, and check out our Code of Conduct.
Anirban is a new contributor. Be nice, and check out our Code of Conduct.
Anirban is a new contributor. Be nice, and check out our Code of Conduct.
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– Yves Daoust
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Hi Yves, sorry - I am new to this site. Haven't yet learnt how to upload a picture. I bungled it this time. I hope to learn it quickly.
$endgroup$
– Anirban
yesterday