Question

Given: JK tangent, KH=16, HE=12 Find: JK.

Answer 1

Answer: $JK=8$

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:

$JK^2=KE*KH$

You know that:

$KH=KE+HE$

Then KE is:

$KE=KH-HE$

$KE=16-12$

$KE=4$

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

$JK^2=4*16\\JK^2=64\\JK=\sqrt{64}\\JK=8$

Answer 2

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