A generalization Napoleon theorem associated with the Kieper

Let ABC be a triangle, F be the first (or secon) Fermat point, let K be the point on the Kiepert hyperbola Let P be the point on line FK. The line through P and perpendicular to BC meet AP at A_0. Define A_0,B_0,C_0 cyclically. Show that A_0B_0C_0 is an equilateral triangle. This triangle homothety to the outer(or inner) Napoleon triangle

 

Đào Thanh Oai

 
Resource Type
Activity
Tags
equilateral  fermat  hyperbola  kiepert  napoleon  point  theorem  triangle 
Target Group (Age)
14 – 18
Language
English
 
 
GeoGebra version
5.0
Views
1340
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