Latest Elitmus Aptitude Question SOLUTION: G is the centroid of triangle ABC . if AG =BC then angle BGC is ?

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(#M40152224) ELITMUS Numerical Ability question geometry Keep an EYE

G is the centroid of triangle ABC . if AG =BC then
angle BGC is ?

Asked In Elitmus shankey (8 years ago)

Solved Soumen Maity Read Solution (7)

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Soumen Maity  (8 years ago) Best Solution

Ans: 90 degree

Solution: It would be easy if I could draw the diagram, but its difficult here. But I am trying my best to explain it.... :)

Centroid cuts the median as 2:1
So, say the median from A cuts the side BC at point at X, then GX= half of AG

now BC= AG, so, GX=BX=CX.
and the angle of GXB=GXC=90 degree.

So, the angle of BGX=45 and angle of CGX=45

So, the angle of BGC= 90 degree.

Pls reply if I am wrong....

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Ishank Chandra  (8 years ago)

90 deg

Soln. Let median from A on side BC via centroid G cuts BC on D, i.e. BD=CD=(1/2)BC.
Since AG:GD=2:1, so GD=(1/2)AG=(1/2)BC as BC=AG given
So, we can say that GD=BD=CD, i.e. tr(GDC) & tr(BGD) are isosceles.
Therefore, ang(GBC)=ang(BGD)=x(say) and ang(GCB)=ang(CGD)=y(say)
Value of angle BGC is reqd, i.e. x+y.
In tr(BGC), ang(GBC)+ang(BGC)+ang(GCB)=180
i.e x+(x+y)+y=180
2x+2y=180
x+y=90=reqd angle BGC

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Ishank Chandra  (8 years ago)

90 deg

Soln. Let median from A on side BC via centroid G cuts BC on D, i.e. BD=CD=(1/2)AD.
Since AG:GD=2:1, so GD=(1/2)AG=(1/2)

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Ananya Pandey  (8 years ago)

90 degree is the right answer

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Shiksha Singh  (8 years ago)

90 dergree is a ryt answer

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ashish sharma  (7 years ago)

soumen maity..how is the angle GXB=GXC=90??

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Garima Pathak  (6 years ago)

Property of centroid G
AG = 2GM

as AG = BC for the given condition
2GM = BC (where M is the midpoint of BC)

thus BM = MG = MC

angles MGB and GBM are equal
angle MGC and GCM too

so MGB + MGC = GBM + GCM
that is
BGC = GBM + GCM

As the sum of all three angles is 180°
angle BGC is 90° and GBM + GCM = 90

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