Question : In a triangle, ABC, the line parallel to BC intersects AB and AC at P and Q respectively. If AB : AP = 5 : 3, then AQ : QC is:

Option 1: 3 : 2

Option 2: 2 : 3

Option 3: 3 : 5

Option 4: 1 : 2

Question : A circle is inscribed in a triangle ABC. It touches sides AB, BC, and AC at points R, P, and Q, respectively. If AQ = 2.6 cm, PC = 2.7 cm, and BR = 3 cm, then the perimeter (in cm) of the triangle $\triangle \mathrm{ABC}$ is:

Option 1: 16.6

Option 2: 33.2

Option 3: 30

Option 4: 28

Question : A circle is inscribed in a triangle ABC. It touches sides AB, BC and AC at points R, P and Q, respectively. If AQ = 3.5 cm, PC = 4.5 cm and BR = 7 cm, then the perimeter (in cm) of the triangle $\triangle \mathrm{ABC}$ is:

Option 1: 30

Option 2: 15

Option 3: 28

Option 4: 45

Question : Let $\triangle ABC \sim \triangle RPQ$ and $\frac{{area}(\triangle {ABC})}{{area}(\triangle {PQR})}=\frac{4}{9}$. If AB = 3 cm, BC = 4 cm and AC = 5 cm, then RP (in cm) is equal to:

Option 1: 6

Option 2: 5

Option 3: 4.5

Option 4: 12

Question : Let $\triangle {ABC} \sim \triangle {RPQ}$ and $\frac{\operatorname{ar}(\triangle A B C)}{\operatorname{ar}(\triangle P Q R)}=\frac{4}{9}$. If ${AB}=3 {~cm}, {BC}=4 {~cm}$ and ${AC}=5 {~cm}$, then ${PQ}$ (in ${cm}$ ) is equal to:

Option 1: 12

Option 2: 4.5

Option 3: 5

Option 4: 6

Question : The sides AB, BC, and AC of a $\triangle {ABC}$ are 12 cm, 8 cm, and 10 cm respectively. A circle is inscribed in the triangle touching AB, BC, and AC at D, E, and F respectively. The difference between the lengths of AD and CE is:

Option 1: 4 cm

Option 2: 5 cm

Option 3: 3 cm

Option 4: 2 cm