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In Fig.9.33, ABC and BDE are two equilateral triangles such that D is the mid-point of BC. If AE intersects BC at F, show that (iii) ar (ABC) = 2 ar (BEC)

Q : 5    In Fig.\small 9.33, ABC and BDE are two equilateral triangles such that D is the mid-point of BC. If AE intersects BC at F, show that

(iii) \small ar(ABC)=2ar(BEC)

[Hint : Join EC and AD. Show that \small BE\parallel AC and  \small DE\parallel AB, etc.]

 

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We already proved that,
ar(\DeltaABC) = 4.ar(\DeltaBDE)   (in part 1)
and, ar(\DeltaBEC) = 2. ar(\DeltaBDE)  (in part ii )

\Rightarrow ar(\Delta ABC) = 2. ar(\DeltaBEC)

Hence proved.

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