Answer:
OL=35
MN=158
Step-by-step explanation:
we know that
The intersecting chords theorem states that the products of the lengths of the line segments on each chord are equal
In this problem
[tex](KO)(OL)=(NO))(OM)[/tex]
[tex](2x+2)(x)=(x-17))(4x)[/tex]
solve for x
[tex]2x^2+2x=4x^2-68x\\4x^2-2x^2-2x-68x=0\\2x^2-70x=0\\2x(x-35)=0[/tex]
The solution is x=35
Verify each statement
1) X=2
The statement is false, because the value of x is 35 units
2) MO=140
The statement is false
Because
[tex]MO=4x=4(35)=140\ units[/tex]
3) OL=35
The statement is true
Because
[tex]OL=x=35\ units[/tex]
4) KL=17
The statement is false
Because
[tex]KL=KO+OL=2x+2+x=3x+2=3(35)+2=72\ units[/tex]
5) MN=158
The statement is true
Because
[tex]MN=MO+ON=4x+x-17=5x-17=5(35)-17=158\ units[/tex]
6) ON=52
The statement is false
Because
[tex]ON=x-17=35-17=18\ units[/tex]
