SSC CPO SI and ASI 2012 Paper

Question : 134 of 200

Marks: +1, -0

If G be the centroid of a triangle ABC such that AG = BC, then the magnitude of ∠BGC is

Solution:

(2) Let M be the midpoint of BC.

Here, AG = 2GM = BC = 2BM = 2MC
In ΔBGM, ∠MBG =∠MGB and
In ΔMGC, ∠MGC = ∠MCG
So,

∠ B G C=\∠ M G B+\∠ M G C

=\∠ M B G+\∠ M C G

Now, in

\Δ B G M, \∠ C B G+\∠ B G C+\∠ B C G=2 \∠B G C=180^{°}

Therefore,

\∠ B G C=90^{\°}

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