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 intersects BC at D and the circumcircle of $\triangle$ABC at E. If AB : AD = 3 : 5, then AE : AC is:

Option 1: 5 : 3

Option 2: 3 : 2

Option 3: 2 : 3

Option 4: 3 : 5

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 : $ABC$ is a triangle and $D$ is a point on the side $BC$. If $BC = 16\mathrm{~cm}$, $BD = 11 \mathrm{~cm}$ and $\angle ADC = \angle BAC$, then the length of $AC$ is equal to:

Option 1: $4 \sqrt{5} \mathrm{~cm}$

Option 2: $4 \mathrm{~cm}$

Option 3: $3 \sqrt{5} \mathrm{~cm}$

Option 4: $5 \mathrm{~cm}$

Question : In a $\triangle$ABC, DE||BC, D and E lie on AB and AC, respectively. If AB = 7 cm and BD = 3 cm, then find BC : DE.

Option 1: 2 : 3

Option 2: 3 : 2

Option 3: 3.5 : 2

Option 4: 7 : 2