Question

A circle touches all the four sides of a quadrilateral ABCD with AB=6 cm,BC=7 cm and CD=4 cm. find AD. ​

Answer 1

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A circle touches all the four sides of a quadrilateral ABCD with AB=6 cm,BC=7 cm and CD=4 cm. find AD.

Step-by-step explanation:

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➣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.

$\therefore ➯AD=3cm$

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