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Answer:
Option (2) 1:6 is the correct option
Step-by-step explanation:
BD:CD = 1:2
ar(∆ABD)/ar(∆ABC) = 1/3
ar(∆ABD) = 1/3×ar(∆ABC)––––(1)
In ∆ABD, BO is the median and median divides the triangle into two triangles if equal areas.
Therefore, ar(∆OAB)=1/2ar(∆ABD)
From equation (1)
ar(∆OAB) = 1/2×1/3 ar(∆ABC)
ar(∆OAB) = 1/6×ar(∆ABC)
ar(∆OAB)/ar(∆ABC) = 1/6
ar(∆OAB):ar(∆ABC) = 1:6
Hope it helped you!
Have a great day!
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