Given 7 points on the plane , what is the maximum number of times we can have the same distance

Question

Assuming the points to be $a_{1},a_{2}\cdots,a_{7}$ we can put them into the vertices and the centre of a regular hexagon, where we can find $12$ distances which are equal and the remaining $9$ distances are non equal. But how can I show that this is the maximum number and it cannot exceed $12$?