doi 10 2478 auom 2014 0029 an s t univ ovidius constant a vol 22 2 2014 37 49 determinant identities and the geometry of lines and circles nicolae anghel ...
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...Doi auom an s t univ ovidius constant a vol determinant identities and the geometry of lines circles nicolae anghel abstract focus this note is nontrivial which typically underlie complex analytic proofs all results in plane after setting up basic dictionary relating to determinants we derive such iden tities connection with four problems steiner line variant euler nine point circle johnson tzitzeica extension certain problem proposed at nd ternational mathematical olympiad amsterdam introduction when it comes solving any there no substitute for elegance concision purely geometric argument yet are situations complexity dictates that approach more desirable even regardless almost always methods can prove be revealing initially intended one only has open introspection purpose reinforce dealing about euclidean certainly huge inventory fascinating type key words numbers m obius transformation international mathematics subject classication primary n c secondary received march revised may ac...