# Circles (A_{42a}) and (A_{42b}): QTB circles

### Definition

Let T be the point on CD beyond D such that CT = AB. Let H be the orthocenter of ATB, also the highest point
of Bankoff's triplet circle (A_{2}). Let A_{42a}
be the midpoint of AH, then A_{42a}
lies on the Nine-Point Circle of ATB. The circle with center A_{42a} through O_{1} is Archimedean. Similarly
we find A_{42b} on BH, and the Archimedean circle with center A_{42b} through O_{2}. These circles
are named after their author Quang Tuan Bui. [Bui 2007]

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