I would say the object you have shown does not have a chord, as the chord is the distance between two points on an arc. You can use the DIST command to obtain the chord of the arc segment, or the distance between the endpoints of the whole object. Similarly, you can use "Aligned dimension" to dimension the chord, or the endpoints of the whole object. To simulate the dimension you have shown, I believe you'd need to dimension the individual segments (see vid below) Or do what you've already done and add the dimension manually as MTEXT.
http://screencast.com/t/imi0YG3u




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