Question

In the figure above, circle o has
center O, diameter AB and a radius of 10,
Line CD is parallel to the diameter. What is
the perimeter of the shaded región​

Answer 1

Answer:

Step-by-step explanation:

Image

In the figure, circle O has center O, diameter AB and a radius of 5. Line CD is parallel to the diameter. What is the perimeter of the shaded region?

A. (53)π+53√(53)π+53

B. (53)π+103√(53)π+103

C. (103)π+53√(103)π+53

D. (103)π+103√(103)π+103

E. (103)π+203√(103)π+203

Since CD is parallel to AB then ∠CBA=∠BCD=30°∠CBA=∠BCD=30° --> ∠CBE=60°∠CBE=60° --> ∠COE=2∗60°=120°∠COE=2∗60°=120° (according to the central angle theorem) --> length of minor arc CE is 120360∗2πr=103∗π120360∗2πr=103∗π;

Now, we should find the lengths of BC and BE (notice that they are equal). Since ∠CBA=30°∠CBA=30° then triangle ACB is 30°-60°-90° right triangle (AB=diameter means that ∠C=90°∠C=90°), thus BCAB=3√2BCAB=32, (BC is opposite to 60 degrees so corresponds to 3√3) --> BC10=3√2BC10=32 (AB = diameter = 2r = 10) --> BC=53√BC=53;

Thus the perimeter of the shaded region is (minor arc CE)+BC+BE(minor arc CE)+BC+BE: 103∗π+53√+53√=103∗π+103√103∗π+53+53=103∗π+103.

Answer: D.