Question

What is the ratio of the length of arc DE to the length of arc BC ?
A: 1/2
B: 1/3
C: 2/5
D: 1/5

Answer 1

The Central angle of a circle is subtended by an arc between those two points. The measure of the arc length is the same as the measure of the central angle of a circle. In this case, we are given two sectors of a circle. The central angle of the larger sector, which subtends arc BC has a measure of \(2\beta\). The central angle of the smaller sector, which subtends arc DE has a measure of \(\beta\). In other words, mARC BC = \(2\beta\) and mARC DE = \(\beta\). Thus the ratio of the length of arc DE to the length of arc BC can be represented by \(\dfrac{\text{m ARC DE}}{\text{m ARC BC}}\)