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Question

In ABC,D is the mid-point of AB and P is any point on BC. CQ||PD meets AB is Q, then prove that area (BPQ)=12 area (ABC)
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Solution

Given that:- In ABC in Which D is the mid point of AB,PD||CQ

Construction:- Join C to D and Q to P.

Proof:- CD is median of the ABC.

ar ( BCD) = ar ( DAC)


In the figure.

PDC and PDQ are on the same base PQ and between the same paralels PD and CQ.


ar ( PDC) = ar ( PDQ)

ar (BCD) = 12ar (ABC)

ar (BPD)+ar (PDC)=12ar (ABC)

ar (BPD)+ar (PDQ)=12ar (ABC)


Hence,

ar(BPQ)=12ar(ABC)


Hence Proved.


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