CDS 2024 · PYQ · Data Sufficiency / Circle and Quadrilateral · medium
A circle touches all the four sides AB, BC, CD, DA of a quadrilateral ABCD. Question: What is the perimeter of the quadrilateral? Statement-I: AB + DC = 10 cm. Statement-II: AD + BC = 10 cm.
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.✓ Correct
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.
Explanation
For a tangential quadrilateral (a circle inscribed touching all four sides), the sum of opposite sides are equal: AB + CD = AD + BC. So perimeter = 2(AB + CD) = 2(AD + BC). Either statement alone gives perimeter = 2 × 10 = 20 cm. Either statement alone suffices.
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