Concurrence

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This is an AoPSWiki Word of the Week for Nov 22-28

Several (that is, three or more) lines (or curves) are said to be concurrent at a point if they all contain that point. The point is said to be the point of concurrence.

Proving concurrence

In analytical geometry, one can find the points of concurrency of any two lines by solving the system of equations of the lines.

Related Theorems

Problems

Introductory

  • Are the lines $y=2x+2$, $y=3x+1$, and $y=5x-1$ concurrent? If so, find the the point of concurrency. (Source)

Intermediate

Olympiad

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