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 : 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

Question : In a circle with centre O, AD is a diameter and AC is a chord. Point B is on AC such that OB = 7 cm and $\angle OBA=60^{\circ}$. If $\angle \mathrm{DOC}=60^{\circ}$, then what is the length of BC?

Option 1: $3 \sqrt{7} \mathrm{~cm}$

Option 2: $3.5 \mathrm{~cm}$

Option 3: $7 \mathrm{~cm}$

Option 4: $5 \sqrt{7} \mathrm{~cm}$

Question : In a triangle ABC, if $\angle B=90^{\circ}, \angle C=45^{\circ}$ and AC = 4 cm, then the value of BC is:

Option 1: $\sqrt{2} \mathrm{~cm}$

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

Option 3: $2 \sqrt{2} \mathrm{~cm}$

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