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Locus of Intersections (Posted on 2012-03-09) Difficulty: 3 of 5
Let ABC be a triangle with points D and E lying on lines AC and AB respectively such that D and E are on the same side of line BC and |BE| = |CD| > 0. Let F be the intersection of rays BD and CE.

What is the locus of the intersections F?

Prove it.

See The Solution Submitted by Bractals    
Rating: 4.0000 (1 votes)

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Initital exploration | Comment 1 of 4
By drawing this on geometer's sketchpad the locus appears to be a line.  I'll assume it is.

This line does not appear to have much to do with the triangle except that it passes through BC.  Also if angle B < angle C the line passes through side AB and if angle C < angle B the line passes through side AC and if the angles are equal the line passes through A.

  Posted by Jer on 2012-03-09 12:06:36
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