MathDB

The towns

A,B,C,D,E

are located clockwise on a circular road such that the distance between

A

and

B

B

and

C

C

and

D

E

and

A

are

5

5

2

1

and

4

km respectively. A health center will be located on that road such that the maximum of the shortest distance to each town will be minimum. How many alternative locations are there for the health center?

<span class='latex-bold'>(A)</span>\ 0 \qquad<span class='latex-bold'>(B)</span>\ 1 \qquad<span class='latex-bold'>(C)</span>\ 2 \qquad<span class='latex-bold'>(D)</span>\ 3 \qquad<span class='latex-bold'>(E)</span>\ \text{None of the preceding}

Problem Statement