JK and LM are perpendicular diameters of a circle. They are each 12 inches long. What is the approximate length of chord LK? With Explanation Please

8.5 inches

Step-by-step explanation:

Let the center of the circle = C

Now CK = CL = 6

Using Pythagoras theorem  

LK^2 = CL^2 + CK^2

        = 6^2 +6^2

          = 36 + 36

          = 72

LK = 72 ^1/2

     = ( 36*2)^1/2

       = 6(2)^1/2

      = 8.5 inches

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)

my apex says that it is false