The circle above has center O, the length of arc is
, and
. What is the length of arc
?
Choice B is correct. The ratio of the lengths of two arcs of a circle is equal to the ratio of the measures of the central angles that subtend the arcs. It’s given that arc is subtended by a central angle with measure 100°. Since the sum of the measures of the angles about a point is 360°, it follows that arc
is subtended by a central angle with measure
. If s is the length of arc
, then s must satisfy the ratio
. Reducing the fraction
to its simplest form gives
. Therefore,
. Multiplying both sides of
by
yields
.
Choice A is incorrect. This is the length of an arc consisting of exactly half of the circle, but arc is greater than half of the circle. Choice C is incorrect. This is the total circumference of the circle. Choice D is incorrect. This is half the length of arc
, not its full length.