Consider a reference triangle Δ A B C and externally inscribe a square on the side B C. Now join the new vertices S_(A B) and S_(A C) of this square with the vertex A, marking the points of intersection Q_(A, B C) and Q_(A, C B). Next, draw lines perpendicular to the side B C through each of Q_(A, B C) and Q_(A, C B). These points cross the sides A B and A C at Q_(A B) and Q_(A C), respectively, resulting in an inscribed square Q_(A, B C) Q_(A, C B) Q_(A B) Q_(A C). The circumcircle through A, Q_(A B), and Q_(A C) is then known as the Lucas A-circles, and repeating the process for other sides gives the corresponding B- and C-circles.

Lucas central triangle | Lucas circles radical circle | Lucas tangents triangle | triangle square inscribing