Topic: Length 'LINE a' equal to Length 'LINE b'

[whdjr]

FACTS:
'LINE a' intesects at the midpoint of 'LINE c'.
'LINE b' intesects at the midpoint of 'LINE d'.
'LINE c' is in a fixed location and length.
'LINE d' and 'LINE b' can move as indicated.

OBJECTIVE:
Length of 'LINE a' needs to equal length of 'LINE b' based on the facts listed above.
Two images are attached with different backgrounds to illustrate the objective.

[Swift]

Can we assume that 'A' is perpendicular to 'C' and that 'B' is perpendicular to 'D'?

[whdjr]

Yes you can assume that and 'LINE a' is @45 deg and 'LINE b' is @0 deg.

[Swift]

what are you wanting to know?

with those constraints you just subtract the length of a from the upper right endpoint coordinate of A to get the other coordinate of B.

[whdjr]

The length of 'LINE a' and 'LINE b' need to be the same.  What distance would you move 'LINE b' and 'LINE d' in the direction shown so that 'LINE a' and 'LINE b' have the same length?

[Swift]

[Jeff_M]

To draw the solution:
Obtain the distance between the intersection of A & C and the intersection of C & D.
Obtain the distance between the intersection of B & D and the intersection of C & D.
Substract the first from the second, a postive value is the distance to move B & D down, a negative is the distance to move B & D up. Once moved, a fillet with R=0 will extend/trim lines A & B and they will be equal in length.

Command: '_dist Specify first point: _endp of  Specify second point: _int of  and
Distance = 408.3907,  Angle in XY Plane = 315,  Angle from XY Plane = 0
Delta X = 288.7758,  Delta Y = -288.7758,   Delta Z = 0.0000

Command:  DIST Specify first point: _int of  and  Specify second point: _endp of
Distance = 509.1399,  Angle in XY Plane = 90,  Angle from XY Plane = 0
Delta X = 0.0000,  Delta Y = 509.1399,   Delta Z = 0.0000

Command: m MOVE
Select objects: Specify opposite corner: 2 found

Select objects:

Specify base point or [Displacement] <Displacement>: _endp of Specify second
point or <use first point as displacement>: @100.7492<270d

Command: f
FILLET
Current settings: Mode = TRIM, Radius = 0.0000
Select first object or [Undo/Polyline/Radius/Trim/Multiple]:
Select second object or shift-select to apply corner:

Command: _list
Select objects: 1 found

Select objects: 1 found, 2 total

Select objects:

                  LINE      Layer: "0"
                            Space: Model space
                   Handle = daf
              from point, X=4899.1352  Y=1960.9711  Z=   0.0000
                to point, X=5018.7501  Y=2080.5860  Z=   0.0000
          Length = 169.1610,  Angle in XY Plane =     45
                  Delta X = 119.6149, Delta Y =  119.6149, Delta Z =   0.0000

                  LINE      Layer: "0"
                            Space: Model space
                   Handle = dab
              from point, X=5187.9110  Y=2080.5860  Z=   0.0000
                to point, X=5018.7501  Y=2080.5860  Z=   0.0000
          Length = 169.1609,  Angle in XY Plane =    180
                  Delta X =-169.1609, Delta Y =    0.0000, Delta Z =   0.0000

There is a small difference in lengths due to rounding errors. But if this were done programtically these would be minimized further.

[Kerry]

Say :
The intersection of Line C and line D is CD.
Then points CA and BD are the same radial distance from CD.
.. or point AB is on a ray that bisects the angle CA CD BD

is that what you were after ?

[whdjr]

Swift and Jeff,

Thank You for your work.  It looked very indepth however I saw it when I saw Kerry's and his was right on the money and very simple.

Kerry,

So simple yet so profound.
Thank You.

[Kerry]

another alternative would be to find the intersection of  line A and line D.
.. then point AB is the midpoint of ray AD AC.

[paulmcz]

Once we know the distance between point AC and line D, let's say X
then A = B = X*(sqrt 2)/(1+(sqrt 2))