Quadrilateral ABCD is circumscribed about a circle. If the

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Quadrilateral ABCD is circumscribed about 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

1. 7.7
2. 16.2
3. 10.7
4. 7.2

Correct Option: A

Since tangents drawn from an exterior point to a circle are equal in length.
∴ AP = AS
BP = BQ
CR = CQ
DR = DS
On adding all these,
AP + BP + CR + DR = AS + BQ + CQ + DS
⇒ (AP + BP) + (CR + DR) = (AS + DS) + (BQ + CQ)
⇒ AB + CD = BC + DA
⇒ 7 + 9.2 = 8.5 + DA
⇒ 16.2 = 8.5 + DA
⇒ DA = 16.2 – 8.5 = 7.7 cm.