The radius of the given circle is 12.1 (correct to the nearest tenth), computed using chord properties.
We assume the radius of this circle to be x.
By the theorem saying that a perpendicular from the center of the circle to a chord, bisects the chord, we can say that CE = ED = 0.5CD = 0.5*18 = 9.
Now, we know that NC = NA = radius of the circle = x.
We are given that AE = 4.
Therefore, NE = NA - AE = x - 4.
Now, in right-angled triangle NEC, by Pythagoras theorem, we can say that,
NC² = CE² + NE²
or, x² = 9² + (x - 4)²
or, x² = 81 + x² - 8x + 16
or, x² - x² + 8x = 97
or, 8x = 97
or, x = 97/8 = 12.125 ≈ 12.1 (correct to the nearest tenth, that is, rounding off up to one decimal place).
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