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Answer:
x ≈ 4.1 cm
Step-by-step explanation:
The segment from the centre to the chord is a perpendicular bisector
The third side of the triangle = 14.6 ÷ 2 = 7.8
We now have a right triangle with legs x and 7.8 with hypotenuse 8.8
Using Pythagoras' identity on the right triangle.
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
x² + 7.8² = 8.8²
x² + 60.84 = 77.44 ( subtract 60.84 from both sides )
x² = 16.6 ( take the square root of both sides )
x = ≈ 4.1 ( nearest tenth )