CDS 2024 · PYQ · Data Sufficiency / Circle Geometry · hard
The chord of a circle of radius R touches at a point on the circumference of a concentric circle of radius r. The length of the chord is 24 units. Question: What are the values of r and R? Statement-I: r is an integer. Statement-II: R is an integer.
A.If the Question can be answered by one of the Statements alone, but not by the other.
B.If the Question can be answered by either Statement alone.
C.If the Question can be answered by using both the Statements together, but cannot be answered by using either Statement alone.
D.If the Question cannot be answered even by using both Statements together.✓ Correct
Explanation
Since the chord of the larger circle is tangent to the smaller (concentric) circle, half-chord = 12, and R² = r² + 144. Many integer pairs satisfy this (r = 5, R = 13; r = 9, R = 15; etc., since R² - r² = 144 has multiple solutions). Even with both statements requiring r and R as integers, multiple solutions exist. Hence the question cannot be answered uniquely even with both statements.
💡 Practice unlimited CDS PYQs + AI-tracked progress on each topic. Sign up free →
Want more CDS practice?
Free daily 10-Q quiz · adaptive mocks · 4,000+ verified PYQs · AI doubt solver in Hindi + English