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Question

$A A_{1^{'}} B B_{1^{'}}$ $C C_{1}$ are the medians of triangle ABC whose centroid is G, if points $A_{1}, C_{1^{'}} G$ and $B_{1}$ are concylic, then

2 b^{2} = a^{2} + c^{2}

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2 c^{2} = a^{2} + b^{2}

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2 a^{2} = a^{2} + c^{2}

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Solution

The correct option is B $2 a^{2} = a^{2} + c^{2}$
As $A A_{1}, B B_{1}$ and $C C_{1}$ are median of $△ A B C$ whose centroid is $G$ .
And as $A_{1}, C_{1} G$ and $B_{1}$ are cyclonic then $c^{2}, a^{2}$ and $b^{2}$ are in A.P.
Thus, $2 b^{2} = a^{2} + c^{2}$

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