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In the adjoining figure, a circle touche...

In the adjoining figure, a circle touches all the four sides of a quadrilateral `ABCD` whose sides are `AB=6cm`, `BC=9cm` and `CD=8cm`. Find the length of side `AD`.

Text Solution

Verified by Experts

When a quadriateral `ABCD` is drawn to circumscribe a circle then `AB+CD=AD+BC`.
`:.AD=AB+CD-BC=(6+8-9)cm=5cm`.
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Knowledge Check

  • In the figure, a circle touches all the four sides of a quadrilateral ABCD whose sides AB= 6.5 cm, BD= 5.4 cm and CD = 5.3 cm . The length of AC is :

    A
    `4.6` cm
    B
    `5.8` cm
    C
    `6.2` cm
    D
    `6.4` cm

  • A circle touches all the sides of a quadrilateral PQRS, whose sides. PQ=2cm, QR =3cm and RS= 4cm. What is the length of PS?

    A
    3 cm
    B
    2 cm
    C
    1 cm
    D
    4 cm

  • Quadrilateral ABCD is circumscribed to a circle. If AB=6cm , BC=7cm and CD=4cm then the length of AD is

    A
    `3cm`
    B
    `4cm`
    C
    `6cm`
    D
    `7cm`