A Fermat Point in Disguise

★ 6/10plane geometryalgebraanalytic geometryTriangle GeometryRotation

Problem

Find the minimum value of

f(x,y)=x2+y2−6y+9+x2+y2+23x+3+x2+y2−23x+3.f(x, y) = \sqrt{x^2 + y^2 - 6y + 9} + \sqrt{x^2 + y^2 + 2\sqrt{3}x + 3} + \sqrt{x^2 + y^2 - 2\sqrt{3}x + 3}.

Answer

Solution

Difficulty6/10
Topicsplane geometry, algebra, analytic geometry, Triangle Geometry, Rotation

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