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

$\text{ \large \underline{ \green{Question:-}}}$

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

Step-by-step explanation:

$\text{ \large \underline{ \blue{Answer:-}}}$

➣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.

$\therefore 》AD = 3cm$

HOPE IT HELPS YOU FRIEND...☺

》》Ⱥʀɳɑѵ♡

Answer 2

Answer:

$\text{ \large \underline{ \purple{Question:-}}}$

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

Step-by-step explanation:

$\text{ \large \underline{ \orange{Answer:-}}}$

➣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.

$\therefore ➯AD = 3cm$

HOPE IT HELPS YOU FRIEND...☺

》》Ⱥʀɳɑѵ♡