Question

# From a point within a triangle, Segments are drawn to the vertices. A necessary.and sufficient condition that the three triangles formed have equal areas, is that the point be: (A) such that the three angles formed each have a measure of 120° (B) the centre of the inscribed circle (C) the centre of the circumscribed circle (D) the intersection of the medians

Answer

The correct answer is Option D. In order for the three triangles formed to have equal areas, it is necessary and sufficient for the point to be the intersection of the medians. Finding the centroid, which is the point where the medians intersect, allows us to divide the triangle into three equal area triangles by connecting the vertices to the centroid. Drawing line segments from a point within the triangle to the vertices will create three triangles with equal areas if and only if the point is the intersection of the medians. For further information on the intersection of medians, please refer to brainly.com/question/29104255 #SPJ4.