  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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