Question

Does the circle A with radius ‘a’ touch circle B with radius ‘b’ internally?

Statement (I): The two circles touch each other at only 1 point
Statement (II): The distance between centers of A and B is a - b

1. Statement (I) ALONE is sufficient, but statement (II) alone is not sufficient to answer the question asked.
2. Statement (II) ALONE is sufficient, but statement (I) alone is not sufficient to answer the question asked.
3. BOTH statements (I) and (II) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
4. EACH statement ALONE is sufficient to answer the question asked.
5. Statements (I) and (II) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Explanatory Answer

Statement I: The two circles touch each other at only 1 point. If two circles touch each other at only one point, they could touch each other either externally or internally. Hence, this statement is not sufficient to answer the question.

Statement II: The distance between the centers of A and B is a - b. If two circles touch each other internally, then the distance between their centers is the difference between their radii.

As statement (II) clearly states that the distance between the centers is a - b, the two circles touch each other internally.

Choice (B) is the correct answer.

Answer Choice (B)