Intersecting Chords Theorem states that the product of the divided lengths of the line segments on each chord are always equal.
In this case, let's say the intersection of US and RT is O :
[tex](UO)(OS)=(RO)(OT)[/tex]
Plug in the values of the segments :
[tex](3x+1)(30)=(x+11)(42)[/tex]
Simplifying the equation :
90x + 30 = 42x + 462
90x - 42x = 462 - 30
48x = 432
x = 9
Substitute x = 9 to US = (3x + 1) + 30
US = [3(9) + 1] + 30
US = 58
The answer is :
US = 58
