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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) is equal to


A

18 Area (Δ ABC)

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B

16 Area (Δ ABC)

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C

14 Area (Δ ABC)

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D

13 Area (Δ ABC)

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Solution

The correct option is A

18 Area (Δ ABC)



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


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