# Circle (A_{16}): The midpoint reflection of Bankoff's triplet circle

### Definition

Reflect (A_{2}) through the midpoint M' of the midpoints M_{1} and M_{2} of the arcs (O_{1}) and
(O_{2}), and the result is the Archimedean circle (A_{16}) [Dodge e.a. 1999].

### Properties

- (A
_{16}) is tangent to the arc (O) at its midpoint M. The circle on diameter M_{1}M_{2} passes
through this point M as well.
- The center A
_{16} lies on OM.
- Let T be the point on CD beyond D such that AB=CT. The center A
_{16}
is the Circumenter of triangle ABT [Bui 2007]

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