x is the radius of the circle. If we draw another radius to the end of the chord, we get a right triangle with legs 12 (half of 24) and 6, and hypotenuse x. We write the Pythagorean Theorem
[tex]x^2 = 12^2 + 6^2 = 144 + 36 = 180[/tex]
[tex]x = \sqrt{180} = \sqrt{36 \times 5} = 6 \sqrt{5}[/tex]
I don't like the calculator part; why ruin a nice exact answer with an approximation? But for completeness
[tex]x \approx 13.4[/tex]
