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Angle subtended at the center by an arc and another angle subtended at the circumference by the same arc: does the resulting figure ($\text{VCOD}$) have a name? The shape is usually shown in most high-school level textbooks, albeit always without specifiying what it's called.

enter image description here

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    $\begingroup$ That looks like a "proof without words" of the inscribed angle theorem $\,\theta= 2 \psi\,$, but I don't know that the figure has any special name or designation. $\endgroup$
    – dxiv
    Commented Nov 10, 2021 at 2:23
  • $\begingroup$ I've heard it called the Star Trek Logo. $\endgroup$
    – Karl
    Commented Nov 10, 2021 at 5:13
  • $\begingroup$ Isn't it okay to just call it a concave quadrilateral? $\endgroup$
    – Sayan Dutta
    Commented Nov 10, 2021 at 6:50
  • $\begingroup$ I guess the fact that the fourth corner is the center of the circle though the other three makes this a specific type of concave quadrilateral. $\endgroup$
    – MvG
    Commented Nov 10, 2021 at 12:08

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This figure is a concave kite, sometimes referred to as a "dart" or an "arrowhead".

A kite — a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are adjacent to each other — may be either convex or concave, but the word "kite" is often restricted to the convex variety. A concave kite is sometimes called a "dart" or "arrowhead", and is a type of pseudotriangle.

Modified excerpt from Kite (geometry), Wikipedia

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  • $\begingroup$ i dont think VCOD is a kite because VC and VD have different side lengths. $\endgroup$
    – cineel
    Commented Mar 21, 2022 at 3:10

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