The radius of a circle measures 12 centimeters what is the area
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See attachment for math work and answer.
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.