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Help Draw Arc of Given Radius Between 2 Points
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* November 23, 2010, 05:44:48 AM
I'm sure it's simple but it eludes me. I've got two perpendicular lines. I need to draw an arc of 1" radius that will touch the lines at 3/4" and 1" from the intersection of those lines. It must be tangent to the point at 1" and pass through the point on the other line at 3/4". Can someone please help the struggling noob. Thanks in advance.  TC Pro 16.
« Last Edit: November 23, 2010, 06:03:34 AM by jimn »

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November 23, 2010, 09:00:15 AM
#1
If the circle doesn't need to be tangent to the two lines, then use the Circle Tan to Entities tool but select the Through Point option to snap the first two points where desired and then enter the radius with an Inspector Bar entry.



* November 23, 2010, 09:32:59 AM
#2
Thanks Don. Exactly what I was looking for. Probably tried every option but that one. I'm not a cad guy but I do need to do some shop drawings occasionally. They just sat me down in front of this thing some months ago and said "figure it out". I've been doing pretty good, but sometimes the little things just get me stymied.

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November 23, 2010, 12:46:50 PM
#3
Hmmmm....I must be misunderstanding something.
     If the circle is tangent to the vertical line at 1" above the horizontal line, and the circle has a radius of 1", it can't pass through any point on the horizontal line other than at 1" along that line; i.e. it must also be tangent to that horizontal line at 1" to the right of the vertical line.
     Notice that the circle in Don's drawing is not tangent to the vertical line at 1" above the horizontal one.

Don Ritchie

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November 23, 2010, 01:13:43 PM
#4
Hmmmm....I must be misunderstanding something.
     If the circle is tangent to the vertical line at 1" above the horizontal line, and the circle has a radius of 1", it can't pass through any point on the horizontal line other than at 1" along that line; i.e. it must also be tangent to that horizontal line at 1" to the right of the vertical line.
     Notice that the circle in Don's drawing is not tangent to the vertical line at 1" above the horizontal one.

The 1" circle can be tangent to the horizontal line at a point that is less than 1" from the vertical line.  In that case, the circle will cross the vertical line at some point below the horizontal line.  That actual distance of the circle's center from the vertical line so that the cross-point is 3/4" below the horizontal line can be calculated with simple trigonometry.

Jeff

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* November 23, 2010, 01:46:16 PM
#5
Hmmmm....I must be misunderstanding something.
     If the circle is tangent to the vertical line at 1" above the horizontal line, and the circle has a radius of 1", it can't pass through any point on the horizontal line other than at 1" along that line; i.e. it must also be tangent to that horizontal line at 1" to the right of the vertical line.
     Notice that the circle in Don's drawing is not tangent to the vertical line at 1" above the horizontal one.

Don Ritchie

Only if the center point of the circle is on a line bisecting the intersection of the two perpendicular lines. In this case it is not.

Thanks for the help everyone.

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November 23, 2010, 03:42:40 PM
#6
Jeff:
 I said, and maintain
Quote
If the circle is tangent to the vertical line at 1" above the horizontal line
then it can't pass through a point on the horizontal line, other than the point of tangency, which is 1" to the right of the vertical line.

Jimn:
     Again, I may not be understanding your original requirements. I understood you to say that the 1" radius circle should be tangent to the vertical line at 1" above the horizontal, and should pass through a point on the horizontal line 3/4" to the right of the vertical line. THAT is impossible.

     To be clear about this, attached is a drawing with a 1" radius circle tangent to the vertical line at 1" above the horizontal line. This is the only circle that can be drawn (right of the vertical line) satisfying those two conditions . It is also tangent to the horizontal line, at 1" to the right of the vertical one, and it's center is 1" above the horizontal line and 1" to the right of the vertical line.

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* November 23, 2010, 04:18:19 PM
#7
Perfect example of how inadequate language can be sometimes.  :) What i actually said was,

"I've got two perpendicular lines. I need to draw an arc of 1" radius that will touch the lines at 3/4" and 1" from the intersection of those lines. It must be tangent to the point at 1" and pass through the point on the other line at 3/4"

To me "tangent" and "pass through" are not the same thing. Sorry for the misunderstanding.

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* November 23, 2010, 04:29:31 PM
#8
Don's point is that the circle is not tangent at the 1" point. Its very nearly tangent, but not quite. Perhaps close enough is good enough, but its good to be sure. The attached shows the tangent line as a dotted line.

Mark

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November 23, 2010, 04:41:17 PM
#9
MarkS:
     Thank you! I was beginning to worry that the new 'fuzzy math' might have re-written trig.

Don Ritchie

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* November 23, 2010, 04:44:34 PM
#10
I thought Don meant that if the circle didn't need to be tangent to BOTH lines then ...


AFAIK any straight line that just touches a curve is "tangent" to that curve. So how is it "nearly tangent". The circle is tangent at one inch and passes through a point at 3/4". Just trying to understand.

I'm not doing the math here just trying to visualize it.
« Last Edit: November 23, 2010, 04:50:09 PM by jimn »

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November 23, 2010, 04:52:52 PM
#11
To remedy what the other have pointed out, then simply use the same tool - left mouse click the left line, then select through point option and then snap the other two points. However your circle will have a radius of 1.04150196345. Close enough?


November 23, 2010, 04:53:58 PM
#12
Jimn said:
Quote
any straight line that just touches a curve is "tangent" to that curve

A tangent to a curve 'just barely' touches the curve ... at a point. If you draw a circle, then draw a straight line tangent to it, you can then draw a perpendicular to the line, at the point of tangency, which MUST pass through the center of the circle.

Try it with TC. Then zoom in on the tangent point .... way in.

Don Ritchie

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* November 23, 2010, 05:01:39 PM
#13
Yup you're right. Got it. The point of tangent is now at a point that is a bit below the 1" mark at the same radius. Thanks.
« Last Edit: November 23, 2010, 05:06:46 PM by jimn »

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