Question

In figure, a circle touches all the four sides of a quadrilateral ABCD whose sides are AB = 6 cm, BC = 7 cm and CD = 4 cm. Find the length of AD.

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Answer 1

Answer:

Given : A circle inscribed in a quadrilateral ,ABCD ,AB=6cm,BC=7cm,CD=4cm.

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To find : AD

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Solution :

Let the circle touch the sides AB,BC,CD,DA, at P,Q,R and S, respectively.

,

AP=AS

BP=BQ

DR=DS

CR=CQ {Lengths of two tangents drawn from an external point of circle, are equal}

Adding all these,

we get,

(AP+BP)+(CR+RD) = (BQ+QC)+(DS+SA)

AB+CD = BC+DA

⇒6+4 = 7+AD

⇒AD=10−7

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=> AD =3cm.

Step-by-step explanation:

Hope it's helpful,,

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