chord length

[tamiatha]

in a circle whose diameter is 20 inches, a chord is 6 inches from the center. what is the length of the chord
need major help on this one
the more adice i get the more confused i get
i need step by step elementary steps
thank you

 

[TchrWill]

in a circle whose diameter is 20 inches, a chord is 6 inches from the center. what is the length of the chord
need major help on this one
the more adice i get the more confused i get
i need step by step elementary steps
thank you


Draw your circle with center O.
Draw the chord AB, 6 inches from the center
Draw a line from the center,O, perpendicular to AB, to point C on AB
Looking at triangle AOC, OC = 6 and OB = 10.
The Pythagorean theorem will get you CB = 8.
Doubling that will give you the length of the chord 16.


Alternatively:
The sine of angle OAC is 6/10 making the angle 36.869º
AB is then 2(10)cos(36.869º) = 8

The following might be of some help to you in similar future problems.

You might also have recognized that the two given triangle sides are multiples of the 3-4-5 Pythagorean Triangle.

R = sector radius
c = chord length
d = distance from center to chord
h = height of segment
s = arc length
µ = sector entral angle, rad.
Ast = segment area
Asr = sector area

Given R and h: µ = 2arccos[(R-h)/R]

Given R and s: µ = s/R

Given R and d: µ = 2arccos[d/R]

Given R and c: µ = 2arsin[c/2R]

Given d and h: R = d + h

Given s and c: c/2s = [sin(µ/2)/µ]

Given s and d: d/s = [cos(µ/2)/µ]

Given c and h: R = [c^2 + 4h^2]/8h

Given c and d: R = sqrt[(4d^2 + c^2)/2]

Given h and s: h/s = [1 - cos(µ/2)]/µ

Given h and µ: R = h/cos(µ/2)

Given µ and d: R = d/cos(µ/2)

Given c and µ: R = c/2sin(µ/2)

s = Rµ

c = 2Rsin(µ/2)

d = Rcos(µ/2)

h = R[1 - cos(µ/2)]

Ast = R^2[µ - sin(µ)]/2

Asr = µR^2/2

Reference: Machine Design, August 22, 1985
Robert Dieckann
Grand Island, NE

 

[soroban]

Hello, tamiatha!

in a circle whose diameter is 20 inches,
a chord is 6 inches from the center.
What is the length of the chord?

              * * *
          *        x  *
        * - - - + - - - *
       *        |     *  *
               6|   *10
      *         | *       *
      *         *         *
      *                   *

       *                 *
        *               *
          *           *
              * * *

Since the diameter is 20, the radius is 10.

See the right triangle?

We have: .$\displaystyle x^2 + 6^2 \:=\:10^2 \quad\Rightarrow\quad x^2 + 36 \:=\:100 \quad\Rightarrow\quad x^2 \:=\:64$

. . Hence: .$\displaystyle x \:=\:8$


Therefore, the length of the chord is: .$\displaystyle 2x \:=\:16$ inches.

 

[ricekrispies]

try this website on video tutorials ( the one your on right now!) i watched it and it shows you exactly how to do it i hope this helps you!
Rice Krispies