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Point A lies on a circle whose center is at point C. Does point B lie inside the circle?
  1. BC2 = AC2 + AB2
  2. ∠CAB is greater than ∠ABC
  • a)
    Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
  • b)
    Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
  • c)
    BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
  • d)
    EACH statement ALONE is sufficient to answer the question asked.
  • e)
    Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Point A lies on a circle whose center is at point C. Does point B lie ...
Steps 1 & 2: Understand Question and Draw Inferences
 
Given: The given information can be represented visually as in the figure above
To find: Does point B lie inside the circle?
  • The answer will be YES if distance between point B and center C is less than the radius of the circle, that is, if BC < r
  • Else, if BC = r or greater than radius r, then the answer will be NO
 
Step 3: Analyze Statement 1 independently
Statement 1 says that ‘BC2 = AC2 + AB2
  • Now, AC = r
  • The minimum possible value of AB = 0 (happens if point B lies ON point A)
  • So, the minimum possible value of BC2 = r2 + 0 = r2
  • Thus, the minimum possible value of BC = r
  • So, BC is equal to or greater than r
  • Therefore, the answer to the question is NO
  • So, Statement 1 alone is sufficient to answer the question
     
Step 4: Analyze Statement 2 independently
Statement 2 says that ‘∠CAB is greater than ∠ABC’
  • In ?ABC, since ‘∠CAB is greater than ∠ABC’, BC > AC
    • (Because we know that the side opposite to the greater angle in a triangle is greater)
  • Therefore, BC > r
  • So, the answer to the question is NO
  • Therefore, Statement 2 alone is sufficient to answer the question
 
Step 5: Analyze Both Statements Together (if needed)
Since we’ve already arrived at a unique answer in each of Steps 3 and 4, this step is not required
Answer: Option D
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Point A lies on a circle whose center is at point C. Does point B lie inside the circle? BC2 = AC2 + AB2 ∠CAB is greater than ∠ABCa)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'D'. Can you explain this answer?
Question Description
Point A lies on a circle whose center is at point C. Does point B lie inside the circle? BC2 = AC2 + AB2 ∠CAB is greater than ∠ABCa)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'D'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Point A lies on a circle whose center is at point C. Does point B lie inside the circle? BC2 = AC2 + AB2 ∠CAB is greater than ∠ABCa)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Point A lies on a circle whose center is at point C. Does point B lie inside the circle? BC2 = AC2 + AB2 ∠CAB is greater than ∠ABCa)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'D'. Can you explain this answer?.
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