Geoville County wants to build a hospital that is equidistant from its three cities L, M, and N. Which construction correctly finds the best location of the hospital?

Construction X because point C is the incenter of ΔLMN
Construction X because point C is the circumcenter of the ΔLMN
Construction Y because point E is the incenter of ΔLMN
Construction Y because point E is the circumcenter of ΔLMN

Construction Y because point E is the circumcenter of ΔLMN

Step-by-step explanation:

we know that

The circumcenter of a triangle is defined as the point where the perpendicular bisectors of the sides of that particular triangle intersects.  

In the construction Y the point E represent the circumcenter of triangle LMN

The distances EM, EL and EN are congruent , because represent the radius of the circle.

That means. that the point E is equidistant from the three vertices

In the context of the problem, the hospital (point E) is equidistant from its three cities L, M, and N        

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