Want to draw a tangent a specific length to two circles that are tangent to two parallel lines.

[jbanasS7XGN]

 

I'm trying to draw a tangent line to two arcs at a distance of 100'. The two arcs are part of circles that have a 300' radius. Each circle is tangent to a line. These lines are parallel and have a distance of 165' between them. The arcs can be shifted down the line as long as it is still tangent to it.  How can I draw it so the tangent line between my arcs is exactly 100'? Attached a picture for reference in case this explanation is confusing. 

[Jason.Piercey]

Maybe using the LENGTHEN command and the TOTAL option will help you establish the 100' length.

[jbanasS7XGN]

Making the tangent off of one circle 100' isn't a problem. The problem is the line be tangent to both circles and be 100'. If I make a line tangent to one circle 100', unless the angle is correct, it will not be tangent to the other circle. 

[pendean]

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@jbanasS7XGN wrote:

Making the tangent off of one circle 100' isn't a problem. The problem is the line be tangent to both circles and be 100'. If I make a line tangent to one circle 100', unless the angle is correct, it will not be tangent to the other circle. 

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You'll have to get into using and turning on CONSTRAINTS: or is this a class homework assignment meant for you to develop manually?

[changmarin]

Here you go.

[jbanasS7XGN]

This does not have to be done manually. For context, you can think of the arcs and parallel lines as centerlines of roads, and I'm trying to reduce the amount of linear feet to the smallest amount possible. 

I've never used constraints before, will look into it and see if I can come up with something. Would be very interested to see the geometrical solution to this problem though. 

[Kent1Cooper]

A is the end/quadrant of an Arc at its tangency to the lower Line.  AB [magenta] is a Line from A going 50' to the right.  OFFSET the white Arc using the Through option, through the Line's right ENDpoint at B, to get the green short-dashed Arc.  C is the CENter of the Arcs.  The grey center-line is halfway between the original Lines.  ROTATE the AB Line using C as the base, with the Reference option -- the Reference direction is from C to B, and the new direction is from C to D, which is the intersection of the green Offset Arc with the grey center-line.

ARRAY the white Arc and the magenta Line, using the Polar option based around D, 2 items to fill 360°.  Join the two 50' Lines into one 100' Line if you like.

[richard_387 · Accepted solution]

Draw one arc, and also a line to its centre. From this point draw orthogonally lines 300 horizontally, 100 vertically and then 300 horizontally. From the centre of the first arc, and with a radius to this last point, strike an arc to the horizontal line of the second arc. Where they intersect is the centre of the second arc.

Draw the arcs and then draw a line tangent to the two arcs. Its length is 100.

[jbanasS7XGN]

Worked perfectly, thanks for this. Can I ask how you figured this out?

[richard_387]

I considered the geometry of the alignment needed.

If one draws a radius, then the tangent is at right angles to it. So I drew the 300 radius line, then the 100 tangent line at right angles to it and then the next 300 radius which is at right angles to the tangent. AutoCAD makes it easy to draw lines at right angles and so the posted shape evolved quite neatly. I could have drawn a 600 line first and then a 100 line at right angles but chose to do it in actual order. If one wanted a different offset, then just draw it.

So a combination of geometry and the AutoCAD facilities for easy drawing made up the final answer.