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Theorem 10.12 : If the sum of a pair of ...

Theorem 10.12 : If the sum of a pair of opposite angles of a quadrilateral is 180º, the quadrilateral is cyclic.

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Since `A`,`B`,`C` are non-collinear, on circle passes through them. Let us draw a circle with center `O`.
Let us assume `D` does not lie on circle.
`ABCD'` is a cyclic quadrilateral.
`/_BAC+/BD'C=180`
But, given that, `/_BAC+/_BDC=180`
Thus,
`/_BD'C=/_BDC`
...
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Knowledge Check

  • The sum of the angles of a quadrilateral is

    A
    180°
    B
    270°
    C
    360°
    D
    300°

  • The sum of angles of a quadrilateral is

    A
    `180^@`
    B
    `360^@`
    C
    `270^@`
    D
    None of the above

  • The sum of all angles of a quadrilateral is

    A
    `180^(@)`
    B
    `270^(@)`
    C
    `360^(@)`
    D
    `480^(@)`

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    The sum of either pair of opposite angles of a cyclic quadrilateral is 180^(@) OR The opposite angles of a cyclic quadrilateral are supplementary.

    Prove that the sum of opposite pair of angles of a cyclic quadrilateral is 180^(@)

    The sum of all the angles of a quadrilateral is

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