SAT Mathematics Practice Test 5

A circle has 360 degrees of arc. In the circle shown, O is the center of the circle and angle AOC is a central angle of the circle. From the figure, the two diameters that meet to form angle AOC are perpendicular, so the measure of angle AOC is $90°$. This central angle intercepts minor arc AC, meaning minor arc AC has $90°$ of arc. Since the circumference (length) of the entire circle is 36, the length of minor arc AC is $\frac{90}{360}\times 36=9$
Choices B, C, and D are incorrect. The perpendicular diameters divide the circumference of the circle into four equal arcs; therefore, minor arc AC is $\frac{1}{4}$of the circumference. However, the lengths in choices B and C are, respectively,$\frac{1}{3}$ and $\frac{1}{2}$ the circumference of the circle, and the length in choice D is the length of the entire circumference. None of these lengths is $\frac{1}{4}$ the circumference.