Thank you for the opportunity to help you with your question!

Mid-point theorem:The midpoints of two adjacent sides of a triangle are jointed by a line segment, which is parallel to the third side and equal to the half of this side.

So MN=AB/2

OM=BC/2

ON=AC/2

perimeter of NOM=OM+MN+ON=(AB+AC+BC)/2

The perimeter of NOM=perimeter of ACB/2

perimeter of NOM=46/2=23

The right answer is b.

Please let me know if you need any clarification. I'm always happy to answer your questions.

Oct 30th, 2015

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