Problem 44386. Circumscribed Pentagon?

Created by goc3

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Building off of Problem 44368, your function will be provided with the five vertices of a regular pentagon (p) as well as the center point (cp) and radius (r) of a circle. The function should return one of the following values:

0: the pentagon is completely enclosed within the circle but is not inscribed
1: the pentagon is inscribed in the circle (within ±0.02)
2: the vertices of the pentagon extend beyond the circle, but its edges still cross back into the circle
3: the pentagon circumscribes the circle (within ±0.02)
4: the pentagon completely encloses, and does not touch, the circle

Points will be rounded to the nearest hundredth. See the test cases for examples.

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Last Solution submitted on Jul 02, 2022

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Osman on 7 Dec 2017

Can there be a mistake about the answer for the last test suite? y_correct is given as 3 so the case where all edges are tangent to circle but when I draw it I see a pentagon that does not touch the circle at all and it is clearly visible without zooming so I don't think error is less than 0.02. I find the answer as y=4 which I think is correct. Can you please check it?

goc3 on 8 Dec 2017

I do believe that it was within the tolerance, though that last case did not touch the pentagon, as you mentioned. I slightly increased the radius in that test case to reduce the gap between the pentagon and circle.

David Verrelli on 5 Jul 2018

Hi, goc3. Nice problem. I have one piece of feedback. I anticipated in a "Cody5:Hard" problem that the pentagon & circle couldn't be assumed to have the same centre if it weren't stated in the problem, but roughly they do seem to share a centre in the present Test Suite. If that is the case, then I suggest either explicitly mentioning it in the Problem Statement, or else adding more test cases where the shapes don't share a centre. An example of the latter would be a tiny circle centred midway along one of the edges of a large pentagon (correct answer 2, but would probably be misclassified if centres assumed equal). Regards, DIV

Svyatoslav Golousov on 7 Sep 2018

Agree with David.
Moreover it is not mentioned that pentagon is regular (didn't check all cases, but most of them are regular).

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Problem 44386. Circumscribed Pentagon?

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