Question

A circle touches all four sides of a quadrilateral ABCD. If AB = 6 cm, BC= 4 cm,CD = 8 cm, find the length of AD

Answer 1

Answer:

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.

Answer 2

Answer:

Step-by-step explanation:

let the circle touch the quadrilateral at the point P, Q, R and S

since the length of the tangents from an external point are equal,

AP=AS   ----(1)

BP=BQ   ----(2)  

DR=DS   ----(3)  

CR=CQ    ----(4)

adding (1),(2),(3) and(4)  

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

AB+CD=BC+DA  

6+4=7+AD

AD=10−7

=3cm.