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In the given figure the sides AB, BE and...

In the given figure the sides AB, BE and CA of triangle ABC touch a circle with centre O and radius r at P,Q and R respectively.
Prove that : `(i) AB+CQ=AC+BQ`
(ii) Area `(triangleABC)=(1)/(2)("Perimeter of"triangleABC)xxr`

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Knowledge Check

  • In figure , the sides AB, BC and CA of triangle ABC, touch a circle at P,Q and R, respectively . If PA = 4 cm , BP = 3 cm and AC = 11 cm , then length of BC is

    A
    11 cm
    B
    15 cm
    C
    14 cm
    D
    10 cm

  • In the figure shown here, a circle touches the side BC of a triangle ABC at P and AB and AC produced at Q and R respectively. What is AQ equal to ?

    A
    One-third of the perimeter of `Delta` ABC.
    B
    Half of the perimeter of `Delta` ABC.
    C
    Two-third of the perimeter of `Delta` ABC
    D
    Three-fourth of the perimeter of `Delta` ABC

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    The side AB, BC and CA of triangle ABC touch a circle at P,Q and R respectively. If PA =4 cm, BP=3 cm and AC=11 cm, then length of BC is

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