Trilinears, together with barycentrics, are used in the modern geometry of the triangle mainly to prove coincidences. Below we summarize the transition functions between some additional coordinate systems related to the trilinears.

Among them the transformation to the

One can locate P using the other ratios QB/QC, RC/RA, SA/SB, related to trilinears by:

Finally one can locate P also from the ratios PQ/AQ, PR/BR, PS/CS, related to trilinears by:

{a,b,c} denote side-lengths and {A,B,C} angle-measures. {h

The

The trilinears of the traces {Q,R,S} can be computed easily from the trilinears (x,y,z) of P and the results of the first section.

Analogously the trilinears of the projections {D,E,F} of P can be easily computed.

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