SOLUTION: If a circle has a diameter of nine inches and a chord that is five inches long, what is the distance from the chord to the center of the circle, to the nearest hundreth of an inch.

Algebra ->  Circles -> SOLUTION: If a circle has a diameter of nine inches and a chord that is five inches long, what is the distance from the chord to the center of the circle, to the nearest hundreth of an inch.      Log On


   

Question 393287: If a circle has a diameter of nine inches and a chord that is five inches long, what is the distance from the chord to the center of the circle, to the nearest hundreth of an inch. There was not a picture in the textbook that went along with this problem. Is there a formula to solve this? If so, what is it? Thank you!
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
picture two radii of the circle
one drawn through the center of the chord
and the other, drawn to the end of the chord

the one through the center of the chord is a perpendicular bisector of the chord

a right triangle is formed by half the chord,
the portion of the radius to the center of the chord (this is the distance from chord to center),
and the radius to the end of the chord (this is the hypotenuse)

by Pythagoras ___ (5/2)^2 + x^2 = (9/2)^2