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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