Răspuns:
In Triunghiurule OBA si OAC => T.F.A. => [tex]\frac{OM}{OA}=\frac{OB}{OC}=\frac{MB}{AC}[/tex]
In Triunghiurile OBA si OCN => T.F.A =>[tex]\frac{OA}{ON}=\frac{OB}{OC}=\frac{AB}{NC}[/tex]
[tex]=> \frac{OM}{OA}=\frac{OB}{OC}[/tex] (1)*
[tex]=>\frac{OA}{ON}=\frac{OB}{OC}[/tex] (2)*
Din (1)* si (2)* => [tex]\frac{OM}{OA}=\frac{OA}{ON}=> OA^2=OM*ON[/tex]
