Given AB is tangent to circle C at point B, what is the circumference of circle C?

Given:

Given that AB is a tangent to circle C.

The length of AB is (2r -1)

The length of AC is (r + 1) + r

The length of BC is r.

We need to determine the circumference of the circle C.

Value of r:

The value of r can be determined using the Pythagorean theorem.

Thus, we have;

Substituting the values, we have;

Simplifying, we have;

Expanding the terms, we get;

Simplifying the values, we have;

Adding both sides of the equation by 4r, we get;

Thus,

Since, the radius of the circle cannot be 0.

Hence, the radius of the circle is 8.

Circumference of the circle:

The circumference of the circle can be determined using the formula,

Substituting r = 8, we get;

Thus, the circumference of the circle is 16π

Hence, Option A is the correct answer.

a) one student is chosen from classroom a, then a student is chosen from classroom b.  

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b.   this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes.   this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes.   this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes.   this makes them dependent events.

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