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Concyclic points are points that all lie on the same circle. This lesson will use some useful theorems to explain how to prove whether or not a set of two, three, or four points are concyclic.

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 · $\begingroup$ Does concyclic just mean there's a circle containing those points? If so, have you learned that any three non-colinear points determine a circle? If so, one naive method would be to find that circle for three of the given points, and check that the fourth is on it. $\endgroup$Reviews: 2.

 · For showing four points are concyclic, one can use complex numbers. If z 0, z 1, z 2, z 3 are complex numbers, the points represented by them are concyclic if and only if. is real. In this case, taking z 0 = − 1 + 4 i, z 1 = 9 + 4 i, z 2 = 3 − 8 i, z 4 = 11, the above ratio is. and hence the points are s: 7.

Concyclic definition is - lying on one and the same circle —used of a system of points.

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  1.  · Concyclic. Four or more points,,,, which lie on a circle are said to be concyclic. Three points are trivially concyclic since three noncollinear points determine a circle (i.e., every triangle has a circumcircle). Ptolemy's theorem can be used to determine if four points are concyclic.. The number of the lattice points which can be picked with no four concyclic is (Guy ).

  2. Concyclic definition, (of a system of points) lying on the circumference of a circle. See more.

  3. In the figure below, we have four concyclic points on the left, and four non-concyclic points on the right. Theorem: If the segment joining two points A and B subtends equal angles at two other points C and D on the same side of AB, then the four points are concyclic.

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