Simson Line Theorem
Simson Line Theorem
In[]:=
H . Takahashi
Simson Line Theorem
Simson Line Theorem
Given a triangle ABE and a point P on the circumcircle of the triangle, the three closest points on each line AB, BC and CE are collinear.
Load Eos
Load Eos
In[]:=
<<EosLoader`
Eos3.7.1.1 (March 21,2023) running under Mathematica 13.2.0 for Mac OS X ARM (64-bit) (November 18, 2022) on Thu 30 Mar 2023 14:38:57.
Construction
Construction
Verification
Verification
We prove that points X, Y and Z are collinear if P is on the circumcircle of ABE.
In[]:=
Goal[SquaredDistance["O","E"]==SquaredDistance["O","P"]CollinearQ[{"X","Y","Z"}]];
In[]:=
map={(*"A"{0,0},"B"{1,0},"C"{1,1},"D"{0,1},*)"E"{u1,v1},"F"{u2,v1},"G"{u3,v3},"P"{u4,v4}};
In[]:=
Prove["Simson theorem",Mappingmap]
Proof is successful.
Simson Line Theorem: Step 11
Out[]=
In[]:=
EndSession[];