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Question-224592




Question Number 224592 by Nicholas666 last updated on 20/Sep/25
Commented by Nicholas666 last updated on 20/Sep/25
     The medians of the triangle ABC  cut it into 6 triangles.                   Prove that the centers of the circum scribed circles                 of these triangles lie ln the same circle.               How is this theorem called?
$$\:\:\:\:\:\mathrm{The}\:\mathrm{medians}\:\mathrm{of}\:\mathrm{the}\:\mathrm{triangle}\:{ABC}\:\:\mathrm{cut}\:\mathrm{it}\:\mathrm{into}\:\mathrm{6}\:\mathrm{triangles}.\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\mathrm{Prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{centers}\:\mathrm{of}\:\mathrm{the}\:\mathrm{circum}\:\mathrm{scribed}\:\mathrm{circles}\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\mathrm{of}\:\mathrm{these}\:\mathrm{triangles}\:\mathrm{lie}\:\mathrm{ln}\:\mathrm{the}\:\mathrm{same}\:\mathrm{circle}.\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\mathrm{How}\:\mathrm{is}\:\mathrm{this}\:\mathrm{theorem}\:\mathrm{called}? \\ $$$$ \\ $$
Commented by mr W last updated on 20/Sep/25
Van Lamoen circle
$${Van}\:{Lamoen}\:{circle} \\ $$
Commented by mr W last updated on 20/Sep/25

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