Question

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Explanation:

Step1: Match diameter to segments

$AB = AC + CB$, and since $AC$ and $CB$ are radii, $AB = 2CB$. But from the given options, since $AC=CB$ (radii), $AB = 2AC$ is equivalent, but from the provided choices, $AB = 2BF$ is not correct, wait no—wait, $AB$ is the diameter, so $AB = AC + CB$, and $AC=CB$, so $AB = 2AC$. But from the options, $AC=CB$, so $AB = 2CB$. But the options have $2BF$? No, wait, no—wait, $AB$ is a diameter, so length $AB = 2 \times$ radius. $AC$ and $CB$ are radii, so $AB = AC + CB = 2AC = 2CB$.

Step2: Match inscribed angle

$\angle ABF$ is an inscribed angle, so its measure is $\frac{1}{2}$ the measure of its intercepted arc $AF$. So $m\angle ABF = \frac{1}{2}$ the measure of arc $AF$.

Step3: Match central angle

$\angle DCB$ is a central angle, so its measure equals the measure of its intercepted arc $DB$. So $m\angle DCB =$ the measure of arc $DB$.

Step4: Match radius segments

$AC$ is a radius, and $CB$ is also a radius of circle $C$, so $AC = CB$.

Answer:

$AB = 2CB$
$m\angle ABF = \frac{1}{2}$ the measure of arc $AF$
$m\angle DCB =$ the measure of arc $DB$
$AC = CB$