Question : In triangle ABC, AD is the angle bisector of angle A. If AB = 8.4 cm, AC = 5.6 cm and DC = 2.8 cm, then the length of side BC will be:

Option 1: 4.2 cm

Option 2: 5.6 cm

Option 3: 7 cm

Option 4: 2.8 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 : O is a point in the interior of $\triangle \mathrm{ABC}$ such that OA = 12 cm, OC = 9 cm, $\angle A O B=\angle B O C=\angle C O A$ and $\angle A B C=60^{\circ}$. What is the length (in cm) of OB?

Option 1: $6 \sqrt{3}$

Option 2: $4 \sqrt{6}$

Option 3: $4 \sqrt{3}$

Option 4: $6 \sqrt{2}$

Question : Suppose $\triangle ABC$ be a right-angled triangle where $\angle A=90°$ and $AD\perp BC$. If the area of $\triangle ABC =40$ cm$^{2}$ and $\triangle ACD =10$ cm$^{2}$ and $\overline{AC}=9$ cm, then the length of $BC$ is:

Option 1: 12 cm

Option 2: 18 cm

Option 3: 4 cm

Option 4: 6 cm

Question : In triangle ABC, $\angle$ B = 90°, and $\angle$C = 45°. If AC = $2 \sqrt{2}$ cm then the length of BC is:

Option 1: 3 cm

Option 2: 2 cm

Option 3: 1 cm

Option 4: 4 cm