perplexus.info :: Just Math : Locus Exploration in Rhombus Realms

Locus Exploration in Rhombus Realms (Posted on 2024-07-27)

Find the locus of the points M that are situated on the plane where a rhombus ABCD lies, and satisfy:

MA·MC + MB·MD = AB²

No Solution Yet Submitted by Danish Ahmed Khan

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Answer, sketch of solution

Comment 1 of 1

M is any point on a line containing one of the diagonals.

Let the rhombus be defined by (a,0) (0,b) (-a,0) (0,-b)

It’s simple to show any point (0,x) will fulfill the constraint.

Posted by Jer on 2024-07-27 17:35:03

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