Respuesta :

luisejr77

Answer: [tex]JK=8[/tex]

Step-by-step explanation:

You can observe in the figure that JK is a tangent and KH is a secant and both intersect at the point K. Then, according to the Intersecting secant-tangent Theorem:

[tex]JK^2=KE*KH[/tex]

You know that:

[tex]KH=KE+HE[/tex]

Then KE is:

[tex]KE=KH-HE[/tex]

[tex]KE=16-12[/tex]

[tex]KE=4[/tex]

Now you can substitute the value of KE and the value of KH into  [tex]JK^2=KE*KH[/tex] and solve for JK. Then the result is:

[tex]JK^2=4*16\\JK^2=64\\JK=\sqrt{64}\\JK=8[/tex]

jamiechen79

Both intersecting point K, JK is a tangent and KH is a secant. You can use the intersecting secant-tangent Theorem:

JK^2=KH*EK

First you can do

KH=EK+EH

KE=4

Then you can substitute.

JK^2=64

JK=8

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