Question 328517
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Let *[tex \Large C_1] represent the center of the larger circle.  Let *[tex \Large C_2] represent the center of the smaller circle.


Let *[tex \Large X] represent the point of intersection of the segments *[tex \Large \overline{C_1C_2}] and *[tex \Large \overline{VW}].


First thing to notice is that *[tex \Large X] is the mid-point of *[tex \Large \overline{VW}].   The next thing to notice is that *[tex \Large \overline{C_1V}] is a radius of circle *[tex \Large C_1].  And that *[tex \Large \overline{C_2V}] is a radius of circle *[tex \Large C_2].  And finally, *[tex \Large \overline{C_1C_2}\ \perp\ \overline{VW}].


*[tex \Large \overline{C_1V}] is the hypotenuse and *[tex \Large \overline{VX}] is the short leg of a right triangle.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ C_1X\ =\ \sqrt{17^2\ -\ 8^2}\ =\ \sqrt{225}\ =\ 15]


Likewise, *[tex \Large \overline{C_2V}] is the hypotenuse and *[tex \Large \overline{VX}] is the short leg of a right triangle.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ C_2X\ =\ \sqrt{10^2\ -\ 8^2}\ =\ \sqrt{36}\ =\ 6]


And finally:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ C_1C_2\ =\ C_1X\ +\ C_2X\ =\ 15\ +\ 6\ =\ 21]


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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