Problem 58956. Find the nine-point circle of a triangle

Created by ChrisR

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Cody Problem 1336 asks us to find the circle that circumscribes a triangle, and Cody Problem 58354 asks us to find the circle that is inscribed in a triangle. This problem deals with the nine-point circle of a triangle—the circle that passes through the midpoints of the sides, the feet of the altitudes, and the midpoints of the line segments connecting the vertices to the orthocenter (the intersection of the altitudes). 
Write a function that takes the x- and y-coordinates of three points describing the vertices of a triangle and returns the center and radius of the nine-point circle, as well as the x- and y-coordinates of the nine points.
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6 Solutions
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Last Solution submitted on Oct 16, 2023

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Tim on 5 Sep 2023

Sorting via x9 is not guaranteed to get results to match--points with the same x value but different y values can be flipped by roundoff errors in x.

ChrisR on 9 Sep 2023

OK, thanks. I think the new test will avoid that problem.

Tim on 10 Sep 2023

Has the test actually changed? Sorry to make extra work for you....

ChrisR on 10 Sep 2023

I thought I had changed it, but it wasn't changed. Now it is. Thanks again. I appreciate the feedback.

Tim on 11 Sep 2023

The new test didn't work for me, but the following seems like it might do the trick:

[~,indx]=sort(angle(complex(x9-x0,y9-y0)));
X9=x9(indx);
Y9=y9(indx);
[~,indx]=sort(angle(complex(x9_correct-x0,y9_correct-y0)));
x9_correct=x9_correct(indx);
y9_correct=y9_correct(indx);

ChrisR on 14 Sep 2023

OK, thanks Tim. I changed the test.

Tim on 16 Sep 2023

Thank you.

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Problem 58956. Find the nine-point circle of a triangle

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Last 200 Solutions

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Problem 58956. Find the nine-point circle of a triangle

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Last 200 Solutions

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Problem Recent Solvers3

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