Question: A circle touches all the four sides AB, BC, CD, DA of a quadrilateral ABCD. What is the perimeter of the quadrilateral?<br>Statement-I: AB+DC=10 cm<br>Statement-II: AD+BC=10 cm

Consider the following for the next ten (10) items that follow : Each item contains a Question followed by two Statements. Answer each item using the following instructions : Choose option (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.

  1. A. If the Question can be answered by one of the Statements alone, but not by the other.
  2. B. If the Question can be answered by either Statement alone. ✓
  3. C. If the Question can be answered by using both the Statements together, but cannot be answered by using either Statement alone.
  4. D. If the Question cannot be answered even by using both Statements together.

Correct Answer: B. If the Question can be answered by either Statement alone.

Explanation

A key property of a tangential quadrilateral (one that circumscribes a circle) is that the sum of opposite sides are equal: AB + CD = AD + BC. The total perimeter is (AB + CD) + (AD + BC). Statement-I gives AB + DC = 10, meaning the perimeter is 10 + 10 = 20 cm. Statement-II gives AD + BC = 10, meaning the perimeter is 10 + 10 = 20 cm. Each statement provides sufficient information independently to find the perimeter.

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