Question : AD is the median of $\triangle$ABC. If O is the centroid and AO = 10 cm, then OD is:

Option 1: 5 cm

Option 2: 20 cm

Option 3: 10 cm

Option 4: 30 cm

Question : In $\triangle$ABC, $\angle$BAC = 90º and AD is perpendicular to BC. If AD = 6 cm and BD = 4 cm, then the length of BC is:

Option 1: 10 cm

Option 2: 12 cm

Option 3: 13 cm

Option 4: 15 cm

Question : In $\triangle \text{ABC}, \mathrm{DE} \| \mathrm{BC}$ and $\frac{\text{AD}}{\text{DB}}=\frac{4}{5}$. If $\mathrm{DE}=12 \mathrm{~cm}$, find the length of $\mathrm{BC}$.

Option 1: 48 cm

Option 2: 12 cm

Option 3: 30 cm

Option 4: 27 cm

Question : Suppose $\triangle A B C$ be a right-angled triangle where $\angle A=90^{\circ}$ and $A D \perp B C$. If area $(\triangle A B C)$ $=80 \mathrm{~cm}^2$ and $BC=16$ cm, then the length of $AD$ is:

Option 1: 10 cm

Option 2: 24 cm

Option 3: 18 cm

Option 4: 12 cm

Question : The centroid of a $\triangle ABC$ is G. The area of $\triangle ABC$ is 60 cm². The area of $\triangle GBC$ is:

Option 1: 10 cm²

Option 2: 30 cm²

Option 3: 40 cm²

Option 4: 20 cm²