Triangle ABC is inscribed in a circle, such that AC is a diameter of the circle (see figure above). If AB has a length of 8 and BC has a length of 15,what is the circumference of the circle?
13π
17π
12π
21π
A
21π
B
12π
C
17π
D
13π
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Solution
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17π: If line segment AC is a diameter of the circle, then inscribed triangle ABC is a right triangle, with AC as the hypotenuse. Therefore, you can apply the Pythagorean Theorem to find the length of AC:
82+152=C2
64+225=c2
289=c2
c=17
You might also have recognized the common 8-15-17 right triangle.
The circumference of the circle is πd, or 17π.
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