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Diagonals AC and BD of a quadrilateral ...

Diagonals `AC` and `BD` of a quadrilateral `ABCD` intersect each other at `P`. Show that`a r\ (A P B)\ xx\ a r\ (C P D)\ =\ a r\ (A P D)\ xx\ a r\ (B P C)dot`

Text Solution

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Let us draw a point `X` and `N` on `BD` such that
`AN_|_BD` and `CX_|_BD`.
Then,
`L.H.S. = ar(APB)xxar(CPD)`
`1/2(AN)(PB)xx1/2(CX)(PD)`
`1/2(AN)(PD)xx1/2(CX)(PB)`
`ar(APD)xxar(BPC) = R.H.S.`
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