Question

Study the diagram of circle O, where JW and JV are tangent to circle O at points W and V, respectively.

If JW=5x+9 and JV=9x+1, what is the length of JV?
Options:
5
2
19

Answer 1

since JW ≅ JV that means

5x+9 = 9x+1
solve for x and then find JV (and also JW!)

Answer 2

19

Answer 3

[AI-generated answer — Explain Bot]

To find the length of JV, we need to find the value of x. Then, we can substitute that value into the equation of JV to get the length.

In the diagram, JW and JV are tangent to the circle O at points W and V, respectively. This means that the tangent line is perpendicular to the radius at the point of contact.

Given that JW = 5x + 9 and JV = 9x + 1, we can set these two expressions equal to each other because they are both tangent segments from the same point, V, to the circle.

5x + 9 = 9x + 1

Now, let's solve this equation for x.

First, we can simplify the equation by combining like terms:

9 - 1 = 9x - 5x

8 = 4x

To isolate x, we divide both sides of the equation by 4:

8/4 = x

x = 2

Now, we have found the value of x as 2. We can substitute this value into the equation of JV:

JV = 9x + 1
JV = 9(2) + 1
JV = 18 + 1
JV = 19

Therefore, the length of JV is 19.

So, the correct option is 19.