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ICSE Class 10 Mathematics Question 19 of 28

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Question 68

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.

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. Maths Competency Focused Practice Questions Class 10 Solutions.
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.