Geometric Art
Details: Click on the figure below.
Saturday, September 17, 2016
Geometry: Nine-Point Circle, Euler Line, Instagram, Mobile Apps
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Geometric Art
Details: Click on the figure below.
In the triangle ABC, we know the centroid G divides Orthocenter H and Circumcenter O in the ratio 2:1
ReplyDeleteThe 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