Circle (A₁₆): The midpoint reflection of Bankoff's triplet circle

Definition

Reflect (A₂) through the midpoint M' of the midpoints M₁ and M₂ of the arcs (O₁) and (O₂), and the result is the Archimedean circle (A₁₆) [Dodge e.a. 1999].

Properties

• (A₁₆) is tangent to the arc (O) at its midpoint M. The circle on diameter M₁M₂ passes through this point M as well.
• The center A₁₆ lies on OM.
• Let T be the point on CD beyond D such that AB=CT. The center A₁₆ is the Circumenter of triangle ABT [Bui 2007]

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