Mathematics
In the given figure, quadrilateral ABCD is circumscribed. The circle touches the sides AB, BC, CD and DA at P, Q, R, S respectively. If AP = 9 cm, BP = 7 cm, CQ = 5 cm and DR = 6 cm, find the perimeter of quadrilateral ABCD.
Answer
We know that,
Tangents from an exterior point to a circle are equal in length.
From A,
AP = AS = 9 cm
From B,
BP = BQ = 7 cm
From C,
CQ = CR = 5 cm
From D,
DR = DS = 6 cm
From figure,
⇒ AB = AP + PB = 9 + 7 = 16 cm
⇒ BC = BQ + QC = 7 + 5 = 12 cm
⇒ CD = CR + RD = 5 + 6 = 11 cm
⇒ DA = AS + SD = 9 + 6 = 15 cm
Perimeter of ABCD = AB + BC + CD + DA
= 16 + 12 + 11 + 15
= 54 cm.
Hence, perimeter of ABCD = 54 cm.
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