Question : All sides of a quadrilateral ABCD touch a circle. If AB = 6 cm, BC = 7.5 cm, CD = 3 cm, then DA is:
Option 1: 3.5 cm
Option 2: 4.5 cm
Option 3: 2.5 cm
Option 4: 1.5 cm
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Correct Answer: 1.5 cm
Solution : A quadrilateral with all sides touching a circle is a tangential quadrilateral. In a tangential quadrilateral, the sum of opposite sides is equal. This property is known as the Pitot theorem. Given that AB = 6 cm, BC = 7.5 cm, and CD = 3 cm. So, AB + CD = BC + DA ⇒ 6 cm + 3 cm = 7.5 cm + DA ⇒ 9 cm = 7.5 cm + DA ⇒ DA = 9 cm – 7.5 cm = 1.5 cm. Hence, the correct answer is 1.5 cm.
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