A circle with center O has a diameter of 14 feet. Points M and N are placed on the circle so that M<mon . Find the length of the intercepted MN.
Use 3.14 for , and round your answer to the nearest tenth.
A. 16.5 ft
B. 18.2 ft
C. 20.4 ft
D. 33 ft
To find the length of the intercepted arc MN, we need to know the degree measure of the angle MOM'n, where M' is the midpoint of MN.
Since the circle has a diameter of 14 feet, the radius (OM) is half of the diameter, which is 7 feet.
Now, let's consider the triangle OMM'. It is a right triangle with the hypotenuse OM and one of the legs being MM'. By using the Pythagorean theorem, we can find the length of MM'.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, OM is the hypotenuse, and MM' is one of the legs.
So, using the Pythagorean theorem:
(OM)^2 = (MM')^2 + (OM')^2
Since OM' is the radius (7 feet), we can rewrite the equation as:
(7)^2 = (MM')^2 + (7)^2
49 = (MM')^2 + 49
Subtracting 49 from both sides:
0 = (MM')^2
Since the length of a line cannot be negative, this equation tells us that MM' has a length of 0. This means that the line segment MN is actually a diameter of the circle.
The intercepted arc MN is therefore the entire circumference of the circle, which can be calculated using the formula:
Circumference = 2πr, where r is the radius
Circumference = 2(3.14)(7) = 43.96 feet
Since the question asks for the length rounded to the nearest tenth, the answer is approximately 43.96 feet, which can be rounded to 44 feet.
So, the correct answer is not given in the options provided.