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In analytical geometry, one can find the points of concurrency of any two lines by solving the system of equations of the lines.
Ceva's Theorem gives a criteria for three cevians of a triangle to be concurrent. In particular, the three altitudes, angle bisectors, medians, symmedians, and perpendicular bisectors (which is not a cevian) of any triangle are concurrent, at the orthocenter, incenter, centroid, circumcenter, and Lemoine point respectively.
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