Mathematics
In the given figure O is the centre of the circle. ABCD is a quadrilateral where sides AB, BC, CD and DA touch the circle at E, F, G and H respectively. If AB = 15 cm, BC = 18 cm and AD = 24 cm, find the length of CD.
Answer
We know that,
The length of tangents drawn from an external point to the circle are equal.
⇒ AE = AH = x (let)
⇒ BE = BF = y (let)
⇒ CF = CG = z (let)
⇒ DG = DH = k (let)
Given,
⇒ AB = 15
⇒ AE + EB = 15
⇒ x + y = 15 …….(1)
⇒ BC = 18
⇒ BF + CF = 18
⇒ y + z = 18 ……..(2)
⇒ AD = 24
⇒ AH + DH = 24
⇒ x + k = 24 ……….(3)
Adding equations (2) and (3), we get :
⇒ y + z + x + k = 18 + 24
⇒ x + y + z + k = 42
⇒ 15 + z + k = 42 [From equation (1)]
⇒ z + k = 42 - 15
⇒ z + k = 27.
⇒ CD = CG + DG = k + z = 27 cm.
Hence, length of CD = 27 cm.
Related Questions
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