In the circle with center D shown below, the length of radius CD is 4 cm, the length of BC is 1 cm, and BC is perpendicular to radius AD at B. When ∠ADC is measured in degrees, which of the following expressions represents the length, in centimeters, of arc AC ?
The correct answer is A.
Arc length is a fractional part of the circumference. That fraction is given by θ/360, where θ is the measure of the central angle, in degrees, intercepting the desired arc.
So, first find the measure of ∠D.
sin ∠D = 1/4
∠D = sin-1(1/4)
The circumference of the circle = 2πr
Therefore, the length of arc AC = [sin-1(1/4)]/360 x 8π
= π/45 sin-1 (1/4)