plotting a circle using points of triangle

[ptc-5041319]

Hello, i am studying master program at mechanical engineering. I am trying plot a circle using 3 points of a triangle. Circle must be plot inside triangle. How can i do? I have done my first homework but second is harder for me. I am using mathcad 15.

[ValeryOchkov]

henry leung wrote:

Can anyone help me to make this file work?

Not anyone - only Werner!

[Werner_E]

Thats exactly the problem with vectors and solve block. Mathcad can not know the dimensions of E and so you would have to provide the elements and again we don't have a pure vetcorial solution.

The best we can achieve is a solution using complex number (similar to Alan's) instead of vectors.

A workaround is attached.

[ValeryOchkov]

Vectors, complex numbers...

KISS- 3 simple (transparent!) equations with 3 unknown r, x.r and y.r. Numerical or symbolic solution and no problem!

See one more animation in attach.

[AlanStevens]

Werner Exinger wrote:

The best we can achieve is a solution using complex number (similar to Alan's) instead of vectors.

Whatever you can do with complex numbers you can do with vectors, of course - see attached. But this still doesn't help with the symbolic solution.

I'm inclined towards Valery's view that his approach is the simplest, especially for novices. That said, there is a pleasing elegance about a vector approach!

Alan

[ValeryOchkov]

The Simplest solution - a cloud function!

Do You know more simple solution this task?

[AlanStevens]

Here's yet another approach (still numerical) that finds the coordinates of the points where the circle touches the triangle at the same time as finding the coordinates of the circle centre and the circle radius.

I think enough is enough though. An interesting problem but time to move on!!

Alan

[ValeryOchkov]

AlanStevens wrote:

I think enough is enough though.

Enough?

And what about this problem in new branch of PlanetPTC:

[AlanStevens]

Ok. Just for you Valery. Here's a 3D version of my previous post. But I'm definitely not going to do anything about a 4D version!

Alan

Message was edited by: ALAN STEVENS Worksheet replaced with a more sensible one!

[ValeryOchkov]

Thanks, Alan!

But...

Einstein said and Werner pointed for us one more that: "Make everything as simple as possible, but not simpler!"

You solution is "simpler"

We have 4 unknowns r, rx, ry and rz and I would like to see the solution of 4 equations, "but not simpler" - 16 equations.

OK!

One subsidiary problem.

We have three segments (or 4), which are known that its are bisectors of one triangle (tetrahedron). Is it possible with a compass (циркуль) and straightedge (линейка), pardon it is unpossible, with Mathad to construct this triangle (tetrahedron)?

.

[AlanStevens]

Valery Ochkov wrote:

One subsidiary problem.

We have three segments (or 4), which are known that its are bisectors of one triangle ...

Do you mean that the angles are bisected or that the sides are bisected?

Alan

[ValeryOchkov]

AlanStevens wrote:

Valery Ochkov wrote:

One subsidiary problem.

We have three segments (or 4), which are known that its are bisectors of one triangle ...

Do you mean that the angles are bisected or that the sides are bisected?

Alan

Angle - a angle bisector, not median.

Sorry for my English.

The angle bisectors crossing is in our triangle a center of our circle.

[AlanStevens]

Valery Ochkov wrote:

Angle - a angle bisector, not median.

Too late! I did both just in case.

I used Heron's formula in both cases - see attached.

Alan

[ValeryOchkov]

AlanStevens wrote:

Valery Ochkov wrote:

Angle - a angle bisector, not median.

Too late! I did both just in case.

Alan

Sorry, not to late - KISS

[AlanStevens]

Very neat - I like it!

Alan

[ValeryOchkov]

AlanStevens wrote:

Very neat - I like it!

Thanks, Alan!

I have a lot of "neat" ideas for the book "Geometry with Mathcad" but no time to do it. And second - it will be good to write this book in English too but Ai knou Inglish not khorosho...

Let us develop this Group - http://communities.ptc.com/groups/fine-math-curves-in-mathvad