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Diagonals AC and BD of a quadrila.teral ABCD intersect each other at P. Show that ar(APBJ x ar(CPDJ = ar(APDJ x ar(BPC). [Hint: From A and C, draw perpendi.culars to BD.]

Diagonals AC and BD of a quadrila.teral ABCD intersect
each other at P. Show that
ar(APBJ x ar(CPDJ = ar(APDJ x ar(BPC).
[Hint: From A and C, draw perpendi.culars to BD.]

Grade:12th pass

1 Answers

Pawan Prajapati
askIITians Faculty 60787 Points
3 years ago
. ar(APB) x ar(CPD) = (ix BP x AL ) (ix PD xCM ) = !. x BP x DP x AL x CM 4 And ar(APD) x ar(BPC) .•.(i) D = !_ x BP x DP x AL x CM ...(ii) From (i) and (ii), we get A B ar(APB) x ar(CPD) = ar(APD) x ar(BPC).

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