G(x)=9x-11 find g(8)
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Check the picture below.
so, the center of the circle is the midpoint of that diametrical segment, and half that length is the radius.
![\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ -2 &,& -4~) % (c,d) &&(~ 3 &,& 8~) \end{array}~~~ % distance value d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[3-(-2)]^2+[8-(-4)]^2}\implies d=\sqrt{(3+2)^2+(8+4)^2} \\\\\\ d=\sqrt{25+144}\implies d=\sqrt{169}\implies d=13\qquad\qquad \qquad \stackrel{radius}{\frac{13}{2}}](https://tex.z-dn.net/?f=%5Cbf%20~~~~~~~~~~~~%5Ctextit%7Bdistance%20between%202%20points%7D%0A%5C%5C%5C%5C%0A%5Cbegin%7Barray%7D%7Bccccccccc%7D%0A%26%26x_1%26%26y_1%26%26x_2%26%26y_2%5C%5C%0A%25%20%20%28a%2Cb%29%0A%26%26%28~%20-2%20%26%2C%26%20-4~%29%20%0A%25%20%20%28c%2Cd%29%0A%26%26%28~%203%20%26%2C%26%208~%29%0A%5Cend%7Barray%7D~~~%20%0A%25%20%20distance%20value%0Ad%20%3D%20%5Csqrt%7B%28%20x_2-%20x_1%29%5E2%20%2B%20%28%20y_2-%20y_1%29%5E2%7D%0A%5C%5C%5C%5C%5C%5C%0Ad%3D%5Csqrt%7B%5B3-%28-2%29%5D%5E2%2B%5B8-%28-4%29%5D%5E2%7D%5Cimplies%20d%3D%5Csqrt%7B%283%2B2%29%5E2%2B%288%2B4%29%5E2%7D%0A%5C%5C%5C%5C%5C%5C%0Ad%3D%5Csqrt%7B25%2B144%7D%5Cimplies%20d%3D%5Csqrt%7B169%7D%5Cimplies%20d%3D13%5Cqquad%5Cqquad%20%5Cqquad%20%20%5Cstackrel%7Bradius%7D%7B%5Cfrac%7B13%7D%7B2%7D%7D)
so, the center of the circle is the midpoint of that diametrical segment, and half that length is the radius.
As you can see in the given figure, there are two intersecting chords inside the circle.
Recall that the "Intersecting Chords Theorem" is given by
For the given case, we have
AE = 7
BE = 6
EC = 9
Let us substitute these values into the above equation and solve for DE
Therefore, the length of DE is 10.5 units.