Skip to main content
OlympiadHQ

Browse · MATH

Print

jmc

algebra intermediate

Problem

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

problem
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 .
Final answer
26\pi