Study the diagram of circle K,
where JL¯¯¯¯¯¯¯
and LM¯¯¯¯¯¯¯¯¯
are tangent to circle K
at points J
and M,
respectively.
Also, JL=3x+10
and ML=7x−6.
The diagram as described in the problem, with radius T L and segment L K drawn. What is the length of LM¯¯¯¯¯¯¯¯¯?
Responses
16
16
22
22
4
4
17.6
4
To find the length of segment LM¯¯¯¯¯¯¯¯¯, we need to find the value of x. Since JL¯¯¯¯¯¯¯ and LM¯¯¯¯¯¯¯¯¯ are tangent to circle K at points J and M, we know that JL and LM are both equal to the radius of circle K, which we will call r.
Therefore, from the given information:
JL = r = 3x + 10
LM = r = 7x - 6
Setting the two equations equal to each other:
3x + 10 = 7x - 6
16 = 4x
x = 4
Now that we have found the value of x, we can substitute it back into either JL or LM to find the length of LM:
LM = 7x - 6
LM = 7(4) - 6
LM = 28 - 6
LM = 22
Therefore, the length of segment LM¯¯¯¯¯¯¯¯¯ is 22.