engleski

Nedian triangle of ratio n

We start with a triangle ABC and a number n in R. On each of the sides of a triangle (in a counterclockwise order), we choose the point that divides the side in ratio n such that AC_n/AB=BA_n/BC=CB_n/CA=n and look at the cevians connecting this point and the opposite vertex. These cevians are called nedians with ratio n. Each pair of the three nedians intersect at a point creating a triangle A_1B_1C_1 called (interior) nedian triangle of ratio n. Using analytic geometry we can find ratios of perimeters, areas, side-lengths etc of this triangle. If we vary the parameter n, we can observe the locus of the vertices of the nedian triangle or its triangle points. We show that this locus lies on the self-isotomic ellipses of the triangle ABC. Furthermore, for a given triangle ABC and a fixed number n we can repeat the construction of the nedian triangle of ratio n on the triangle A_1B_1C_1 and so on. We will analyse properties of these iteration.

triangle, cevian, nedian, interior nedian trinagle, isotomic point

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