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- W2555001447 abstract "Given a triangle ABC, we solve the construction problem of a point P , together with points Bc, Cb on BC, Ca, Ac on CA, and Ab, Ba on AB such that PB aCa, Ab PC b, and AcBcP are congruent triangles similar to ABC. There are altogether seven such triads. If these three congruent triangles are all oppositely similar to ABC, then P must be the procircumcenter, with trilinear coordinates (a 2 cos A : b 2 cos B : c 2 cos C). If at least one of the triangles in the triad is directly similar to ABC, then P is either a vertex or the midpoint of a side of the tangential triangle. We also determine the ratio of similarity in each case." @default.
- W2555001447 created "2016-11-30" @default.
- W2555001447 creator A5028527740 @default.
- W2555001447 date "2003-01-01" @default.
- W2555001447 modified "2023-09-27" @default.
- W2555001447 title "On the Procircumcenter and Related Points" @default.
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- W2555001447 hasPublicationYear "2003" @default.
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