Diagonals AC and BD of a quadrilateral ABCD intersect each other at P. – InterviewSolution

InterviewSolution

1.	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`
Answer» 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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