How do I draw a circle tangent to 3 points on a shape?

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Hey, can anyone help me with this project? I need to draw a circle tangent to 3 points on the red shape in the image I attached. The circle's diameter needs to represent the longest distance between 2 points on the shape. The question I have is: I don't know how to look for these 3 points on the shape. I also don't know how to find the 2 points on the shape which represents the longest distance inside of the shape. So how do I draw the circle? I am so frustrated with this. Anyone who can help me I would appreciate a lot. Thank you so much!!!

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Use CIRCLE command with 3Point option, then manually specify TANgent OSNAP 3times while picking the 3 points.

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Thanks! The problem I have is that I cannot find the exact location of those 3 points. The diameter of the circle has to represent the longest distance between any 2 points on the outline of the red shape. Any tools I can use? Thank you!

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Command: CIRCLE

Specify center point for circle or [3P/2P/Ttr (tan tan radius)]: 3P

Specify first point on circle: _tan to

Specify second point on circle: _tan to

Specify third point on circle: _tan to

Command:

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There is only one possible circle that will be tangent three times for that shape, but I'm not sure if the diameter will necessarily represent the longest distance, unless the shape was defined that way.

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Command: CIRCLE

Specify center point for circle or [3P/2P/Ttr (tan tan radius)]: 3P

Specify first point on circle: _tan to

Specify second point on circle: _tan to

Specify third point on circle: _tan to

Command:

[ATTACH=CONFIG]52870[/ATTACH]

Thank you Nestly! Let me thy this method to other shapes and give you a feedback.

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I agree with RobDraw that a circle tangent at three points along the shape may not be tangent at the maximum width. For a better understanding of the geometry try the following. Draw a circle with a diameter that is your best guess of the maximum distance. Position this circle with its center ON the red shape. Then make many copies of this circle with centers on the red shape (use OSNAP NEAREST). The center of the tangent circle is in the area where the multiple arcs come closest. This may not yield an arc with three tangent points to the red shape.

You can experiment with different diameter circles to determine an approximate three tangent circle.

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