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 Locus of Intersections (Posted on 2012-03-09)
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)

Comments: ( Back to comment list | You must be logged in to post comments.)
 re: Initital exploration | Comment 2 of 4 |
(In reply to Initital exploration by Jer)

`I've found a problem with Sketchpad whenconstructing loci. With respect to thisproblem, let point D on line CA be theindependent variable. To locate point Eon line AB I construct a circle with Bas the center and radius |CD|. This circleintersects line AB at two points. In realtime it's easy to pick which to label E,but when running the locus Sketchpad hasno way to determine which point to pick.Therefore, I end up creating the locusin two steps: 1) pick point D on the sameside of line BC as vertex A and 2) pickpoint D on the other side. Have you run into this problem when creating loci?`
` `

 Posted by Bractals on 2012-03-09 15:09:04

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