The Intersecting Chords theorem states that the products of the line segments on each chord are equal. In other words,
[tex]UM\cdot UN=UJ\cdot UK[/tex]
We already know that UM = 26, UJ = 13, and UK = 39. Putting these values in the above equation gives us
[tex]26\cdot UN=13\cdot39[/tex][tex]26\cdot UN=507[/tex]
Dividing both sides by 26 gives
[tex]\textcolor{#FF7968}{UN=19.5.}[/tex]
which is our answer!
