Assignment 6: Explorations With Geometer's Sketch

Ebru Ersari

Given line segments j, k, m. If these are the medians of a triangle, construct the triangle.

Since the given segments are the medians of our triangle, I constructed each side of the triangle, first. For constructing each side, I have used the circles. I took the length of the segments j, k, m as the radius and drew 3 circles. The diameter of each circles are the length of each side of our triangles. I named the length of the diameters as n, o, p.
n = 2j
o = 2k
p = 2m

Then, I have constructed another three circles with radius n, o, p.
The purple circle’s radius is n = 2j. I have constructed the green circle as the same centered with the purple circle. The green circle’s radius is o=2k. Lastly, I have constructed the blue circle.

Now, I got a segment with n + o + p (2j + 2k + 2m) length.

I chose the base as the segment o = 2k. Since purple and green circles have the same center, I drew the segment from the center of these two circles to the intersection of blue and purple circles. The length of these segment is n =2j since it is the radius of the purple circle. I had two segments, one is o and the other is n. When I drew the third side of the triangle, the length of this side is p = 2m because it is the radius of the blue circle.

The circles and the triangle with length 2j+2k+2l are below.