Saturday, September 17, 2016

Geometry: Nine-Point Circle, Euler Line, Instagram, Mobile Apps

Geometric Art

Details: Click on the figure below.

Geometry: Nine-Point Circle, Euler Line, Instagram, Mobile Apps.

1 comment:

  1. In the triangle ABC, we know the centroid G divides Orthocenter H and Circumcenter O in the ratio 2:1
    The Medal triangle MaMbMc is similar to ABC but its centroid remains the same i.e G
    We can see that Ma is projection of A along the lines BMb, CMc and similarly Mb is projection of B and Mc is projection of C
    Hence O is the projection of H along the lines passing through the centroid.

    So in the Medal triangle, O is the orthocenter and N is the circumcenter
    Hence OG = 2NG => If NG = 1 => OG = 2 => NO = NG+GO = 3
    But GH = 2OG => GH = NG + NH = 2*2 = 4 => NH = 4-1=3

    Hence center of the Nine point circle of triangle ABC is the midpoint of the Euler line

    ReplyDelete