A nice generalization of the Simson line theorem

A nice generalization of the Simson line theorem Problem 1: Let ABC be a triangle, let a line L through circumecenter, let a point P lie on circumcircle. Let AP,BP,CP meets L at A_P, B_P, C_P. Denote A_0,B_0,C_0 are projection (mean perpendicular foot) of A_P, B_P, C_P to BC,CA,AB respectively. Then A_0,B_0,C_0 are collinear. - When (l) pass through P, this line is Simson line. Problem 2: The new line \overline {A_0B_0C_0} bisect the orthocenter and P

 

Đào Thanh Oai

 
Materialtyp
Aktivität
Tags
collinear  line  simson  theorem 
Zielgruppe (Alter)
14 – 18
Sprache
English
 
 
GeoGebra Version
5.0
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2628
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