Centroid Divides Median in the Ratio 2:1

Q.

If $\mathrm{S}$ is circumcenter, $\mathrm{G}$ the centroid, $\mathrm{O}$ the orthocenter of $∆\mathrm{ABC}$, then $\mathrm{SA}+\mathrm{SB}+\mathrm{SC}$ is equal to:

1. $SG$

2. $OS$

3. $SO$

4. $OG$

Q.

In $△ABC,AD,BE$ and $CF$ are medians, and $G$ is centroid. If $AD=15cm$, find $AG$.

1. $5cm$
2. $10cm$
3. $8cm$
4. $12cm$

Q. In $\Delta$ ABC, the medians BE and CF intersect at G. AD is a line meeting BC at D. If GD is 1.5 cm, then find the value of AD.

1. 2.5 cm
2. 3 cm
3. 4 cm
4. 4.5 cm

Q.

The following figure has centroid at the point O

If AO = 6 cm , find the length of OR.

1. 5 cm

2. 2 cm

3. 3 cm

4. 12 cm

Q.

In triangle ABC the medians AD and BE intersect at G. If AD = 12 cm, then AG = ____ cm

1. 18 cm

2. 10 cm

3. 8 cm

4. 9 cm

Q.

In triangle ABC, the medians AD and BE intersect at G. If AD = 18 cm, then GD = ____ cm

1. 6

2. 8

3. 12

4. 14

Q.

The given triangle has Centroid at O.

If PC = 54 cm, Find the length of OC.

1. 18 cm

2. 24 cm

3. 36 cm

4. 42 cm

Q.

In any triangle, the point of intersection of the medians divides each median in the ratio of _____ .

1. 3 : 2

2. 2 : 1

3. 1 : 3

4. 3 : 1

Q. The centroid of a triangle is located 12 units from one of the vertices of a triangle. Find the length of the median of the triangle drawn from that same vertex.

1. 16 units
2. 18 units
3. 24 units
4. 36 units

Q.

The ratio in which the Centroid of the triangle divides the median is _____.

1. 3 : 1

2. 2 : 1

3. 1 : 1

4. 3 : 2