MathDB

Point chosen from a locus of points

Source:

December 13, 2019

Locusgeometryanalytic geometryinfimum

Problem Statement

Let

M

be a point in the interior of a triangle

ABC,

let

D

be the intersection of

AM

with

BC,

let

E

be the intersection of

M

with AC, let

F

be the intersection of

CM

with

AB.

Knowing that the expression

\frac{MA}{MD}\cdot \frac{MB}{ME}\cdot \frac{MC}{MF}

is minimized, describe the point

M.

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