Question

А circle touches all four sides of a quadrilateral ABCD whose side AB= 6cm, BC = 7cm and CD=4cm. Find AD.​

Answer 1

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.