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If G is the centroid of ΔABC and AG = BC, then ∠BGC is: (SSC CGL 2nd Sit. 2012)
- a)75°
- b)45°
- c)90°
- d)60°
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
If G is the centroid of ΔABC and AG = BC, then ∠BGC is: (SSC...
In ΔABC
Given AG = BC
i.e., GD = BD = DC
In ΔBGD
BD = DG ∴ ∠GBD = ∠DGB …(i)
In ΔCGD
GD = DC, ∴ ∠GCD = ∠DGC …(ii)
∠GBD + ∠DGB + ∠DGC + ∠DCG = 180
2(∠BGD + ∠CGD) = 180
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Community Answer
If G is the centroid of ΔABC and AG = BC, then ∠BGC is: (SSC...
Given:
- G is the centroid of ΔABC
- AG = BC
To Find:
Find the measure of ∠BGC
Solution:
Properties of a Centroid:
- The centroid of a triangle divides each median into segments in a 2:1 ratio
- In other words, AG = 2(GG') and BG = 2(GC)
Given AG = BC:
AG = 2(GG') and BC = BC
Since AG = BC, we can equate the two:
2(GG') = BC
Dividing BC into two equal parts:
Since GG' is half of BC and BG = 2(GC), then BG = BC/2
∠BGC is a right angle:
In a triangle, the centroid G divides the median into a 2:1 ratio. Therefore, BG = 2(GC). This implies that ∠BGC is a right angle (90°).
Therefore, the measure of ∠BGC is 90°.
- G is the centroid of ΔABC
- AG = BC
To Find:
Find the measure of ∠BGC
Solution:
Properties of a Centroid:
- The centroid of a triangle divides each median into segments in a 2:1 ratio
- In other words, AG = 2(GG') and BG = 2(GC)
Given AG = BC:
AG = 2(GG') and BC = BC
Since AG = BC, we can equate the two:
2(GG') = BC
Dividing BC into two equal parts:
Since GG' is half of BC and BG = 2(GC), then BG = BC/2
∠BGC is a right angle:
In a triangle, the centroid G divides the median into a 2:1 ratio. Therefore, BG = 2(GC). This implies that ∠BGC is a right angle (90°).
Therefore, the measure of ∠BGC is 90°.
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If G is the centroid of ΔABC and AG = BC, then ∠BGC is: (SSC CGL 2nd Sit. 2012)a)75°b)45°c)90°d)60°Correct answer is option 'C'. Can you explain this answer?
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