Dao’s Theorem on Six Circumcenters associated with a Cyclic Hexagon

Theorem

Let $A_i, i = 1, 2,..., 6$, be six points on a circle. Taking subscripts modulo $6$, we denote, for $i = 1, 2,..., 6$, the intersection of the lines $A_iA_{i+1}$ and $A_{i+2}A_{i+3}$ by $B_{i+3}$, and the circumcenter of the triangle AiAi+1Bi+2 by $C_{i+3}$. The lines $C_1C_4, C_2C_5, C_3C_6$ are concurrent.

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