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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". ( http://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.)2011-01-10
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    What leads you to believe that this object should have a name?2011-01-10
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    I call this a "slice" ;)2011-01-10
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    @Jasper Loy "By '(round) disk' do you simply mean circle", well, a circle is one-dimensional; I meant the thing it bounds.2011-01-10
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    @Day Late Don "a cleaner description": Yes, thanks!2011-01-10
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    Well, I like "Carl".2014-03-23

2 Answers 2

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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.2011-01-09
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    @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'?2011-01-09
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    If you "don't know the answer", please delete your answer.2013-11-26
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    @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...2013-11-26
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    @TonyK Someone else did. It showed up in the [10k Tools](http://math.stackexchange.com/tools). Rest assured, it's nothing personal.2013-11-26
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    I appreciate your honesty. +12015-09-06