The semicircle above has a radius of r inches, The distance between the chord and the diameter in terms of r is √5 r/3 inches.
What is chord of Circle ?
A chord of a circle can be defined as a line segment connecting any two points on the circumference. It should be noted that the diameter is the longest chord of a circle which passes through the center of the circle.
To find the distance required one can use either the Pythagorean theorem or the trigonometric ratios. Let the semicircle have center O. The diameter AB has length 2r. Because chord CD is 2/3 of the length of the diameter,
CD=2/3(2r) = 4r/3
let the distance between diameter AB and chord CD be x inches. To find x draw a right triangle connecting center O, the midpoint, E of chord CD, and point C . Using Pythagorean theorem here,
r² = x² + (CD/2)²
=> r² = x² + (2r/3)²
=> r² = x² + 4r²/9
=> x² = r² - 4r²/9 = 5r²/9
=> x = √5 r/3
Hence, the distance between the chord and the diameter in terms of r is √5r/3..
To learn more about chord of circle , refer:
https://brainly.com/question/7805618
#SPJ4
