Important: Since AB and CD are both diameters, their point of intersection (point O) must be the center of the circle.

Let's use some useful circle properties

First let's add a blue line, to divide ∠CEB into 2 angles



CD is the DIAMETER of the circle
Since ∠CED is an inscribed angle containing (aka "holding") the diameter, we can conclude that ∠CED = 90°



Now recognize that the intersection of AB and CD creates two equal (vertically opposite) angles, we can conclude the angle opposite the 48° is also 48°



Now recognize that we have two angles containing (aka "holding") the arc BD
Property: If a CENTRAL angle and an INSCRIBED angle contain the same arc, then the CENTRAL angle is TWICE the INSCRIBED angle
This means that ∠DEB = 24°


At this point, we have:

So, ∠CEB = 90° + 24° = 114°

Answer: A

RELATED VIDEO