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Let P be a point, not the center, in the interior of a (round) disk D⊂ℝ² and let A and B be points on ∂D such that the line segments AP and BP have equal length. Choose an arc AB. What's the shape bounded by the arc and the two segments called?

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For $P$ at the center, that's a "sector". ( en.wikipedia.org/wiki/Circular_sector ) I don't know of a name for $P$ elsewhere. How about "pseudo-sector" or "generalized sector"? (BTW, this might be a cleaner description: Given P on the diameter bisecting arc AB, the figure bounded by AP, BP, and arc AB.) –  Blue Jan 10 '11 at 0:02
What leads you to believe that this object should have a name? –  Tpofofn Jan 10 '11 at 1:07
I call this a "slice" ;) –  Matt Calhoun Jan 10 '11 at 1:25
@Jasper Loy "By '(round) disk' do you simply mean circle", well, a circle is one-dimensional; I meant the thing it bounds. –  msh210 Jan 10 '11 at 16:39
@Day Late Don "a cleaner description": Yes, thanks! –  msh210 Jan 10 '11 at 16:42
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2 Answers

I suppose you could call it an isosceles curvilinear triangle, although that doesn't capture the curvy part being an arc of a circle.

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It's called a circular segment.

Edited to add: As Jasper has pointed out in the comments, this is not what the question asked. So I don't know the answer.

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I'm pretty sure that a circular segment is only the region between a chord AB and minor arc AB. –  Isaac Jan 9 '11 at 21:42
@Isaac: Yes, my Wikipedia link agrees with you. It looks as if the region between a chord AB and major arc AB doesn't have a name. How about 'circular cosegment'? –  TonyK Jan 9 '11 at 22:17
If you "don't know the answer", please delete your answer. –  Lord_Farin Nov 26 '13 at 9:17
@Lord_Farin: I don't know what inspired you to check back through almost three years of my answers, but I'm sure it's not healthy... –  TonyK Nov 26 '13 at 9:38
@TonyK Someone else did. It showed up in the 10k Tools. Rest assured, it's nothing personal. –  Lord_Farin Nov 26 '13 at 9:39
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