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M2_8_8_1_1

GeoGebra Construction

8.1.1

Explore various positions for the vertices of the triangle and the points L, M, and N to verify the following result: If three proper Cevian lines are concurrent, then d= 1. Find examples of concurrent Cevian lines in which all three of the points L, M, and N lie on the triangle triangle ABC and other examples in which at least one of the three points is not on triangle ABC. Verify that d=1 in all cases in which the proper Cevians are concurrent.

Solution:

When the three lines are concurrent, d=1. I could not find an example where at least one of the three points was not on triangle ABC and the value of d was 1.