Mathematics
In the given figure, the circle touches the sides AB, BC, CD and DA of a quadrilateral ABCD at the points P, Q, R and S respectively. If AB = 11 cm, BC = x cm, CR = 4 cm and AS = 6 cm, find the value of x.
Circles
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Answer
We know that,
Tangents from an exterior point to a circle are equal in length.
From A,
⇒ AP = AS = 6 cm
From C,
⇒ CR = CQ = 4 cm
⇒ BP = AB - AP = 11 - 6 = 5 cm.
From B,
⇒ BQ = BP = 5 cm
From figure,
BC = BQ + CQ = 5 + 4 = 9 cm
x = 9 cm
Hence, x = 9 cm.
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