In the circle with center D, the length of radius CD is 4 cm

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 ?

Answer

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

= 2π(4)

= 8π

Therefore, the length of arc AC = [sin^-1(1/4)]/360 x 8π

= π/45 sin^-1 (1/4)