New Year's Countdown Day 16: Six Teens

Six teenagers--Henry, Ingrid, Jerry, Katherine, Liam, Monica--stand in a circle to toss around a frisbee. Three cones are placed on the ground that act as goalposts for the teens to toss the frisbee at.

The first cone is placed at the midpoint of the segment connecting Henry and Katherine. It turns out that Ingrid, Liam, and the first cone are in a straight line, as well as Jerry, Monica, and the first cone. Then, the other cones are placed along the line connecting Henry and Katherine so that the second cone is on the line connecting Ingrid and Jerry, and the third cone is on the line connecting Liam and Monica.

If the distance between the first and second cones is 16 meters, then find the sum of the possible distances, in meters, between the second and third cones. Round to the nearest tenth. (If you think there are infinitely many possible distances between the second and third cones, input -1 as your answer.)

This problem is part of the set New Year's Countdown 2017 .