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algebra intermediate
Problem
What is the circumference of the circle with center at and passing through ? Express your answer in terms of .

Solution
To find the circumference, we must first find the length of the radius, . We can do this by using the distance formula or by noticing that the points , , and form a right triangle with legs of length 5 and 12. This is a Pythagorean triple, so the hypotenuse must equal 13.
Now that we know the radius has length 13, the circumference is .
Now that we know the radius has length 13, the circumference is .
Final answer
26\pi