perplexus.info :: Geometry : Equidistant point

Equidistant point (Posted on 2018-06-03)

Given a triangle ABC and a straight line L.

Find the point P on L such that
PA²+PB²+PC² is the smallest.

No Solution Yet Submitted by Ady TZIDON

Rating: 3.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

re(2): one messy method

| Comment 3 of 4 |

(In reply to re: one messy method by Steven Lord)

Ah! The math reduces even more simply:

If a,b,c are the location of points on L that are the the dropped perpendiculars of A, B, C, then P is located at the average of these three points.

Posted by Steven Lord on 2018-06-05 06:26:21

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