Question : Three medians AD, BE, and CF of $\triangle ABC$ intersect at G. The area of $\triangle ABC$ is $36\text{ cm}^2$. Then the area of $\triangle CGE$ is:

Option 1: $12\text{ cm}^2$

Option 2: $6\text{ cm}^2$

Option 3: $9\text{ cm}^2$

Option 4: $18\text{ cm}^2$

Question : In a $\triangle ABC$, AD, BE and CF are the medians from vertices A, B, and C, respectively. The point of intersection of AD, BE and CF is called

Option 1: median point

Option 2: orthocentre

Option 3: centroid

Option 4: incentre

Question : $\triangle ABC$ is a triangle. PQ is a line segment intersecting AB in P and AC in Q and PQ || BC. The ratio of AP : BP = 3 : 5 and the length of PQ is 18 cm. The length of BC is:

Option 1: 28 cm

Option 2: 48 cm

Option 3: 84 cm

Option 4: 42 cm

Question : In $\triangle$ABC the height CD intersects AB at D. The mid-points of AB and BC are P and Q, respectively. If AD = 8 cm and CD = 6 cm then the length of PQ is:

Option 1: 3 cm

Option 2: 7 cm

Option 3: 9 cm

Option 4: 5 cm

Question : In $\triangle ABC$, D and E are the midpoints of sides BC and AC, respectively. AD and BE intersect at G at the right angle. If AD = 18 cm and BE=12 cm, then the length of DC (in cm ) is:

Option 1: 10

Option 2: 6

Option 3: 9

Option 4: 8