Question : The quadrilateral ABCD is circumscribed by a circle. If the lengths of AB, BC, and CD are 7 cm, 8.5 cm, and 9.2 cm, respectively, then the length (in cm) of DA is:
Option 1: 7.7
Option 2: 16.2
Option 3: 10.7
Option 4: 7.2
Correct Answer: 7.7
Solution :
Given: The quadrilateral ABCD is circumscribed by a circle. The lengths of AB, BC, and CD are 7 cm, 8.5 cm, and 9.2 cm, respectively.
Since tangents drawn from an external point are always equal,
So, AP = AS, BP = BQ, CR = CQ, and DR = DS
By adding these we get,
⇒ AB + CD = BC + AD
⇒ AD = (7 + 9.2) – 8.5 = 7.7 cm
Hence, the correct answer is 7.7.
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