Let ABCbe a triangle. Points D,E,F are t...

Let ABCbe a triangle. Points D,E,F are taken on the sides AB,BC and CA respectively such that `(AD)/(AB)=(BE)/(BC)/=(CF)/(CA)=alpha` Prove that the vectors AE, B and CD form a triangle also find alpha for which the area of the triangle formed by these is least.

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Let ABCbe a triangle. Points D,E,F are taken on the sides AB,BC and CA respectively such that `(AD)/(AB)=(BE)/(BC)/=(CF)/(CA)=alpha` Prove that the vectors AE, B and CD form a triangle also find alpha for which the area of the triangle formed by these is least.

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