In mathematics, a cyclic quadrilateral is one whose vertices all lie on the same circle. In other words, every vertex is on the circumcircle of the other three. For more information, see the MathWorld article.
These quadrilaterals are cyclic:
This trapezoid is not cyclic.
(Images from Wikipedia)
Given the coordinates of four vertices in counterclockwise order which form a convex quadrilateral, determine if the quadrilateral is cyclic.
Coordinates will be integers (note, however, that the circumcenter coordinates and circumradius are not necessarily integers.) As implied by the previous paragraph, no three points will be co-linear and no two coincident.
You may take input using any reasonable format. In particular,
[[x1,y1],[x2,y2],[x3,y3],[x4,y4]] and complex numbers are all fine.
Output using any different consistent values for true and false.
[0,0], [314,0], [314,1], [0,1] [-5,5], [5,-5], [1337,42], [42,1337] [104, -233], [109, -232], [112, -231], [123, -224]
[0,0], [314,0], [314,100], [0,99] [31,41],[59,26],[53,58],[0,314]