Let's make a diagram to illustrate the given information.
Notice that CD passes through the center of the circle, which means it lies on a diameter. Also, because CD⊥AB, we get that CD bisects AB. Then, AC=CB=6 inches.
Next, if E is the other endpoint of the diameter DE, we can apply the Segments of Chords Theorem to set the following equation.
DC* CE = AC* CB
Let's substitute the corresponding measures to find CE.
Finally, we calculate the diameter of the circle by using the Segment Addition Postulate.
d = DC + CE ⇒ d &= 9+4
⇒ d &= 13
In consequence, the diameter of the original cake was 13 inches.
