A Cellular Triangle Containing a Specified Point
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Let P be a set of finite points in the plane in general position, and let x be a point which is not contained in any of the lines passing through at least two points of P. A line l is said to be a k-bisector if both of the two closed half-planes determined by l contain at least k points of P. We show that if any line passing through x is a \(\)-bisector and does not contain two or more points of P, then there exist three points P1, P2, P3 of P such that ΔP1P2P3 contains x and does not contain points of P in its interior, and such that each of the lines passing through two of them is a \(\)-bisector.
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