Question

Select the following statements that are true.

X=2
MO=140
OL=35
KL=17
MN=158
ON=52

Answer 1

MO=140

OL=35

and MN=158

Explanation:

Answer 2

OL=35

MN=158

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

`(KO)(OL)=(NO))(OM)`

`(2x+2)(x)=(x-17))(4x)`

solve for x

`2x^2+2x=4x^2-68x\\4x^2-2x^2-2x-68x=0\\2x^2-70x=0\\2x(x-35)=0`

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

`MO=4x=4(35)=140\ units`

3) OL=35

The statement is true

Because

`OL=x=35\ units`

4) KL=17

The statement is false

Because

`KL=KO+OL=2x+2+x=3x+2=3(35)+2=72\ units`

5) MN=158

The statement is true

Because

`MN=MO+ON=4x+x-17=5x-17=5(35)-17=158\ units`

6) ON=52

The statement is false

Because

`ON=x-17=35-17=18\ units`