Ellipse-inscribed family of cyclic quadrilaterals: vertex centroid is stationary

Описание к видео Ellipse-inscribed family of cyclic quadrilaterals: vertex centroid is stationary

Let E be an ellipse, P(t) a point on its boundary, and O a fixed point. Consider the family of circles K(t) centered on O and passing through P(t). For a suitable choice of O (e.g., near the center of E), the K(t) will have three real intersections A(t),B(t),C(t) with E. Consider the quadrilaterals Q(t)=[P, A, B, C]. The video shows that their vertex centroid C0=(P+A+B+C)/4 is stationary over P(t).

GGB : https://www.geogebra.org/classic/zka7...

Комментарии

Информация по комментариям в разработке

Похожие видео