Question

Circle C has center O, and a chord AB such that ∠AOB = 80 degrees. Does point E lie inside the circle?

Statement (I): ∠AEB > 50 degrees
Statement (II): ∠AEB < 30 degrees

1. If the question can be answered with statement I alone but not statement II alone, or can be answered with statement II alone but not statement I alone
2. If the question cannot be answered with statement I alone or with statement II alone, but can be answered if both statements are used together
3. If the question can be answered with either statement alone
4. If the question cannot be answered with the information provided

Explanatory Answer

Statement (I): ∠AEB > 50 degrees.
INSUFFICIENT. E could lie on the minor segment ADB or slightly outside or slightly inside the circle.

Statement (II): ∠AEB < 30 degrees.
SUFFICIENT. All the angles inside the circle will be in the range from 40 – 140 degrees. Anything less than 40 will have to be outside the circle.

Answer Choice (A)