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In mathematics, biangular coordinates are a coordinate system for the plane where C 1 {\displaystyle C_{1}} and C 2 {\displaystyle C_{2}} are two fixed points, and the position of a point P not on the line C 1 C 2 ¯ {\displaystyle {\overline {C_{1}C_{2}}}} is determined by the angles ∠ P C 1 C 2 {\displaystyle \angle PC_{1}C_{2}} and ∠ P C 2 C 1 . {\displaystyle \angle PC_{2}C_{1}.}