The length of segment FC (the distance from the center of the circle to the chord) is approximately 10.1 cm to the nearest tenth.
In order to answer this question, we need to find the length of segment FC, which is not directly given. Assuming this is a common geometry problem, it seems like we want to find the distance from the chord to the center of the circle (this is often denoted FC in geometry problems).
The chord and the diameter suggest that we might be able to apply right triangle principles or the properties of a circle to find this length.
Now, we can use the property that the perpendicular from the center of the circle to a chord bisects the chord. Hence, EC = CD/2 = 18 cm / 2 = 9 cm.
We want to find FE, which is the distance from the center of the circle to the chord CD.
We also know that the radius of the circle is half of the diameter, so FA =
FB = FD = FC = 27 cm / 2 = 13.5 cm.
Now, we can use the Pythagorean theorem to solve for FE:
FE^2 + EC^2 = FC^2
We know EC and FC, so:
FE^2 + 9^2 = 13.5^2
FE^2 + 81 = 182.25
FE^2 = 182.25 - 81
FE^2 = 101.25
Taking the square root of both sides to solve for FE:
FE = sqrt(101.25)
FE ≈ 10.1 (to the nearest tenth)
Therefore, the length of segment FC (the distance from the center of the circle to the chord) is approximately 10.1 cm to the nearest tenth.