UPSC CDS I 2024 Math Paper

Concept:For a quadrilateral that has an incircle (touches all four sides), the sums of lengths of opposite sides are equal.Explanation:Given quadrilateral $\text{ABCD}$ has a circle touching all four sides, so it is a tangential quadrilateral.In any tangential quadrilateral, $AB + DC = AD + BC$.The perimeter is $AB + BC + CD + DA = (AB + DC) + (AD + BC)$.Statement I gives $AB + DC = 10$ cm. Then $AD + BC$ also equals $10$ cm. So perimeter = $10 + 10 = 20$ cm.Statement II gives $AD + BC = 10$ cm. Then $AB + DC$ also equals $10$ cm. So perimeter = $10 + 10 = 20$ cm.Thus either statement alone provides enough information to compute the perimeter.Answer:Option B – The question can be answered by either statement alone.