Could someone please provide a solution with proof to this problem???

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Could someone please provide a solution with proof to this problem???

Can any ellipse be represented as a diagonal half cross section of a cylinder? By "diagonal half cross section" I mean if a plane cuts the cylinder through these 3 points: a point from the top circle, the centre, and the diametrically opposite point of the first point. I know there are 2 cases of this, but right now I can't provide a picture of the case I want from the two. Sorry for that. I want the case where the plane cuts the curved surface of the cylinder, not the plane surfaces on both sides. I hope you understand.

If the answer is yes, that any ellipse can be represented like this, then can't we measure the perimeter of the ellipse from this? Because the distance between the point from the top circle and the diametrically opposite point should be measured by applying the pythagorean formula, right? Because the cylinder can be opened and can be made into a rectangle. Am I right? I think I am wrong somewhere. But I don't know where. I've searched and found out that there's no exact formula for calculating the perimeter of an ellipse.

Sorry that I can't make it more understandable :( If you have difficulty understanding what I am asking, you may go to the links below and maybe you will get the idea which I am talking about.

You can check the figures here. Though I don't want the cross section area, I want the perimeter.

And maybe this and this to get what I wanted by diagonal half cross section.

Thanks in advance...

I have code of finding the perpendicular distance from a point to a 3D plane. But in this case, the plane is infinite. If the plane is not infinite, but limited to a certain piece, such as the face of an object, then how to find the minimum distance from a point to that face?

An example:

If the 3 points defining a "piece" of plane are:

**1 0 0**

**0 1 0**

**0 0 0**

And the query point is:

**1 1 1**

Then the answer will be .

Is there any implementation in C++ for this problem? If yes, then could someone please provide it? And if not, then sharing the idea of solving it will also help. Thanks in advance.

Can anyone please help me in this one? I am getting WA on test 24 and I can't find any mistake in my idea. Has anyone faced the same verdict in test 24? Maybe it's corner case or something. I'd be really grateful if someone helped me out. I am trying it from this afternoon without any break and now I'm frustrated :(

Here's the link to the problem.

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