Circles with a specific tangent

[darkstarmedia]

I am trying to put two circles together so that the tangent line is 90 degrees from vertical (aka 270 or 80 degrees) . the circles are o different sizes.... any suggestions... I was hoping to create the tangent line and "stick" but there is no automated stick...

Richard

[Tech2]

I gather you want to place the two circles so there is a 0 deg (horizontal) line tangent to both circles and an 80 deg line tangent to both circles.

Interesting problem.

Other viewers might want to try their hand at this without reading further.

It's easy to create the two tangents to the small circle. The problem is how to position the large circle to satisfy two constraints simultaneously: being tangent to the 80 deg line and being tangent to the 0 deg line. First, we shift the problem to the center of the large circle - the center must simultaneously lie on a line parallel to the 80 deg line and on a line parallel to the 0 deg line, the distance between each pair of parallel lines being the radius of the large circle. The center of the large circle can be placed simultaneously on those two new lines by placing the center at the intersection of those lines. That can be done with the snap-to-intersection capability. Following this strategy proceed as follows:

* Draw a horizontal line (0 deg) from the bottom snap point of the small circle to the right, past the large circle.
* Edit | Copy ... Edit |Paste (to make a duplicate).
* Rotate the copy 80 degrees CCW around the snap center of the small circle (so that it remains tangent). (See [-- login to view link --] ).
* Edit | Copy ... Edit | Paste (to make a duplicate).
* Rotate the copy 90 degrees CCW (to 170 deg) around the upper end point.

That was the easy part. Now for the sub-problem of placing a circle tangent to two straight lines:

* Move the large circle so its center snaps to the upper end of the 80 deg line.
* Select the 170 deg line.
* Line | Intersect and delete the segment outside the circle.
* Select the 80 deg line.
* Edit | Copy ... Edit | Paste (to make a duplicate).
* Move the copy so its top end snaps to the right end of the radius line of the large circle. The center of the large circle must ultimately lie somewhere along this line in order to be tangent to the 80 deg line.
* Move the large circle so the bottom snaps to the bottom of the small circle.
* Draw a horizontal line from the center of the large circle to the right past other lines. The center of the large circle must ultimately lie somewhere along this line in order to be tangent to the 0 deg line.
* Move the large circle so its center snaps to the intersection of the upper horizontal line and the rightmost 80 deg line. This is the only point that satisfies the two constraints.
* Edit | Select All
* Line | Intersect.
* Delete the superfluous lines.

That's the "professional" solution. These types of problems can be solved more simply if you don't need a "perfect" solution. For example, in the above case after drawing the two tangents to the small circle:

* Move the large circle so the bottom snaps to the bottom of the small circle.
* Set the Nudge value on the numeric bar to .001".
* Nudge the large circle right while using the Zoom feature to look closely at the tangency to the 80 deg line. Make sure the 80 deg line intersects with the large circle.
* Edit | Select All
* Line | Intersect.
* Delete the superfluous lines.

More examples of solving 2D drawing problems can be found at:
[-- login to view link --]

[darkstarmedia]

Thanx!!!!!

Richard

[Tech2]

For the sub-problem of placing a circle tangent to two straight lines here is another solution:

* Extend the straight lines so they cross.
* Move the circle so its center snaps to the vertex.
* Do Line | Repeat twice.
* Move one of the duplicate circles so its center snaps to the intersection of the original circle and one of the straight lines.
* Move the other duplicate circle so its center snaps to the intersection of the original circle and the other straight line.
* Select the original circle and one of the other circles.
* Line | Tangent
* Select the original circle and the other other circle.
* Line | Tangent
* Delete the circles not at the vertex.
* Move the circle to the intersection of the tangents.
* Delete the tangents.