Circumcenter of a Triangle
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Uploader Comments (khanacademy)
All Comments (13)
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wish khan academy was a real school.
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wow... i just started circumcenter of a triangle in class... :)
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Great!
But how to find the center of a circle incide a triangle, which touches triangle's edges?
Would it always be the same center as the circumcenter in this video? If not, when would they be the same?
Thanks.
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@AlRoderick : Good point. So yes, the circumcenter could be far outside the triangle--and it would represent a HUGE circle (as big as you please, actually). So...circumcenters can easily be outside their area....I infer that all triangles with all apexes on a circle ALL share the same circumcenter, and, of course, it's at the center of the circle. Thanks!
Pretty interesting and counter-intuitive (for me). Perhaps this points toward the connection between pi and trigonometry and triangles.
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@GetMeThere1 Think of it like this. The perpendicular bisectors are lines, so they go on forever in both directions. If the triangle has two small angles and one big one, say 10 degrees, 20 degrees and 150 degrees, the lines wouldn't intersect until well outside the triangle, because the lines continue on forever outside the triangle. The circumcenter would be past the side opposite the big angle.
The important bit is that all the points of the triangle are on the circle edge, not inside it.
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I don't believe this. The school told me I couldn't comprehend Geometry and refused to let me take it in 10th grade.
If they would have DONE the examples like THIS, I wouldn't have had a problem, b/c I understood THIS. So I don't see how it's MY problem.
I think it was THEIRS.
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oh! amazing khan.i like it.than you khan.
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@khanacademy : Ah! OK, cool. I'd like to hear more...
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I've never heard of this before. Cool! But it prompts me to ask: does ANY triangle drawn in a circle have its circumcenter at the center of the circle? And, of course, the answer is obviously: "No." I can draw a triangle in a circle whose area doesn't even COVER the center of the circle.
....which then makes me ask: Do all possible triangles drawn in a circle that DO cover the center of the circle share their circumcenters? Again, no, because I can imagine a triangle that wouldn't work...
GetMeThere1 4 months ago
@GetMeThere1 Actually, this is a good topic for a video. You can have a triangle where the circumcenter is outside of the triangle.
khanacademy 4 months ago