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Asked by  | 26th Jan, 2009, 11:32: AM

Expert Answer:

Draw any quadrilateral as given in the question.

Now , as construction,

 Draw  AM perpendicular to BP

 and

 CN perpendicular to DP

We know that are of a triangle = 1/2* base * altitude

So,

LHS=

 Area(triangle APB)*Area(triangle CPD)

=[(1/2)*BP*AM] [(1/2)DP*CN]

=[(1/2)*PD*AM] [(1/2)*BP*CN]

Area(triangle APD)*  Area(triangle BPC)

=RHS

Hence proved.

Note that

for both trianglesAPB and ADP, AM is the height

Similarly

 for both triangles CPD and  BPC, CN is the height.

Answered by  | 27th Jan, 2009, 06:06: PM

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