Question : In triangle ABC, the bisector of angle BAC cuts the side BC at D. If AB = 10 cm, and AC = 14 cm, then what is BD : DC?

Option 1: 10 : 7

Option 2: 5 : 7

Option 3: 7 : 5

Option 4: 7 : 10

Question : In triangle ABC, the bisector of angle BAC cuts the side BC at D. If AB = 10 cm, and AC = 14 cm then what is BD : BC ?

Option 1: 5 : 3

Option 2: 7 : 5

Option 3: 5 : 2

Option 4: 5 : 7

Question : ABC is a right angle triangle and $\angle ABC = 90^{\circ}$. BD is perpendicular on the side AC. What is the value of $(BD)^2$?

Option 1: $AD\times DC$

Option 2: $BC\times AB$

Option 3: $BC\times CD$

Option 4: $AD\times AC$

Question : Triangle ABC and DEF are similar. If AB = 92 cm, BC = 48 cm, AC =120 cm, and the length of the smallest side of triangle DEF is 200 cm, then find the length of the longest side of triangle DEF.

Option 1: 400 cm

Option 2: 225 cm

Option 3: 350 cm

Option 4: 500 cm

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