Question

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

Answer 1

Answer:

AD=3 cm

Step-by-step explanation:

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

To find : AD

Proof : 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=3cm.

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