Question

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?

• A. $21\pi$
• B. $13\pi$
• C. $12\pi$
• D. $17\pi$

Answer 1

Answer: (D)

$17\pi$

17$\pi$: 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:

$8^2+{15}^2=C^2$

$64+225=c^2$

$289=c^2$

$c=17$

You might also have recognized the common 8-15-17 right triangle.

The circumference of the circle is $\pi d$, or $17\pi$.