[alogo] Vecten (6)

Consider the Vecten configuration of triangle ABC. Show that triangles ABC and LMN are perspective, their perspectivity center (P : Vecten point of the triangle ABC) lying in the line joining their circumcenters J and Q respectively. Show also that the ratio k = |PJ|/|PQ| is always greater or equal to sqrt(3)+1, the equality being valid only in the case ABC is equilateral. Look at Vecten.html for the definitions. The triangles LMN and OST are anti-similar with respect to P, their similarity ratio being k.

[0_0] [0_1] [0_2] [0_3]
[1_0] [1_1] [1_2] [1_3]
[2_0] [2_1] [2_2] [2_3]
[3_0] [3_1] [3_2] [3_3]

Look at Vecten_Equilateral.html for the case of the Vecten configuration, constructed on an equilateral triangle.

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