# Circles (A_{29a}) and (A_{29b}): The first Radical line pair

### Definition

Let A(C) be the circle through C with center A and (O') the Midway semicircle on diameter O_{1}O_{2}.
The circle with center on the radical line of A(C) and (O) and tangent to both (O') and A(C) is Archimedean. Similarly
the circle with center on the radical line of B(C) and (O) and tangent to both (O') and B(C) is Archimedean [van Lamoen 2006].

### Properties

- The common tangent of (A
_{29a}) and A(C) passes through O_{2} and the common tangent of (A_{29b})
and B(C) passes through O_{1} . [van Lamoen 2006]

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