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Question

D is the mid-point of side BC of ΔABC and E is the mid point of BD. If O is the midpoint of AE.Then Area of (ΔBOE) .

A
18 Area(ΔABC)
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B
16 Area(ΔABC)
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C
14 Area(ΔABC)
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D
13 Area(ΔABC)
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Solution

The correct option is A 18 Area(ΔABC)

Since AD is the median,
2ar(ΔABD)=ar(ΔABC) ...(i)
Similarly, 2ar(ΔABE)=ar(ΔABD)...(ii)
And 2ar(ΔBOE)=ar(ΔABE)...(iii)
Now, ar(ΔABC)=2ar(ΔABD)
=2[2ar(ΔABE)] from (ii)
=4[2ar(ΔBOE)] from (iii)
=8ar(ΔBOE)
18ar(ΔABC)=ar(ΔBOE)

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