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Abstract

In this article we will obtain a formula for the area of the triangle inscribed by three straight lines that pass through the vertexes of a given triangle. Using the formula we can prove C'eva`s theorem. We obtain formulas that calculate the areas of the six triangles that are part of the given triangle; in case that the three transported lines meet in one point. The calculation method depends on the notion of limits, so that this notion could be illustrated to students in a fine geometrical method. We define the term “three fair points with respect to a given triangle” to illustrate the three points on the edges of a triangle; so that the three lines that join them to the opposite triangle vertexes meet in one point. We define the term “a fair triangle with respect to a given triangle” to be a triangle whose vertexes are three fair points. We show that the maximal area fair triangle with respect to a given triangle is the triangle whose vertexes are the middle points of the given triangle.