Question

Find the measure of CD. Round to the nearest tenth. mCD=[?]degrees

Answer 1

Answer:

m(arc CD) = 14.1 cm

Step-by-step explanation:

Measure of an arc of the circle = $\frac{\theta}{360}(2\pi r)$

Here 'r' = radius of the circle

θ = Angle subtended by the arc at the center of the circle

From triangle OED,

sin(∠EOD) = $\frac{ED}{OD}$

sin(∠EOD) = $\frac{\frac{12.7}{2}}{9.06}$

                 = $\frac{6.35}{9.06}$

                 = 0.7

m∠EOD = 44.498

              ≈ 44.5°

Angle subtended by the arc CD at the center = m∠COD

                                                                            = 2(44.5)

                                                                            = 89°

m(arc CD) = $\frac{89}{360}(2\pi)(9.06)$

                 = 14.07

                 ≈ 14.1 cm