Question:
Two concentric circles have the same centre O. A chord on the outer circle AE intersects the inner circle in points B and D. C is a point on the segment BD. What is the ratio of AC to CE?
Statement A
A. Ratio of lengths of BC to CD is 1.
Statement B
B. A third circle intersects the inner circle at B and D. C is on the line joining the centres of the third and inner circle.
Two concentric circles have the same centre O. A chord on the outer circle AE intersects the inner circle in points B and D. C is a point on the segment BD. What is the ratio of AC to CE?
Statement A
A. Ratio of lengths of BC to CD is 1.
Statement B
B. A third circle intersects the inner circle at B and D. C is on the line joining the centres of the third and inner circle.
Statement A
A. Ratio of lengths of BC to CD is 1.
Statement B
B. A third circle intersects the inner circle at B and D. C is on the line joining the centres of the third and inner circle.
Show Hint
Symmetry properties in circle chords often yield exact segment ratios without extra construction.
Updated On: Aug 5, 2025
- The question can be answered by one of the statements alone but not by the other.
- The question can be answered by using either statement alone.
- The question can be answered by using both the statements together, but cannot be answered by using either statement alone.
- The question cannot be answered even by using both statements together.
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The Correct Option is A
Solution and Explanation
From Statement A: $BC = CD$ implies C is midpoint of BD, enough to determine AC:CE ratio using symmetry.
From Statement B alone: The position of C is only partially described, insufficient to find the exact ratio without more data.
Hence, only Statement A alone is sufficient.
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