Question

$km$ is tangent to $odot j$. what is $jm$?

Explanation:

Step1: Identify right triangle property

Since $KM$ is tangent to $\odot J$, $\angle MKJ = 90^\circ$, so $\triangle MKJ$ is a right triangle.

Step2: Apply Pythagorean theorem

For right $\triangle MKJ$, $JM^2 = KM^2 + JK^2$.
Substitute $KM=12$, $JK=16$:
$$JM^2 = 12^2 + 16^2$$
$$JM^2 = 144 + 256$$
$$JM^2 = 400$$

Step3: Solve for $JM$

Take square root of both sides:
$$JM = \sqrt{400} = 20$$

Answer:

20 yd