Consider a triangle in which we draw line segments connecting the vertices of the triangle to the points of tangency of the incircle on the opposite sides. This divides the original triangle into six 'daughter' triangles.
If one of these daughter triangles is an equilateral triangle, then find the ratio of the area of the original triangle to that of the equilateral daughter triangle.
Answers
Answer:
To divide a triangle into three triangles of equal area is to find the centroid (the point where the medians intersect). After determining the centroid (point G below), construct the segments connecting the vertices to the centroid. The three triangle created are of equal area.
So from a point within a triangle, line segments are drawn to the vertices. A necessary and sufficient condition that the three triangles thus formed have equal areas is that the point be the intersection of the medians of the triangle
Answer:
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