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 : ABC is a right-angled triangle with AB = 6 cm and BC = 8 cm. A circle with centre O has been inscribed inside $\triangle ABC$. The radius of the circle is:

Option 1: 1 cm

Option 2: 2 cm

Option 3: 3 cm

Option 4: 4 cm

Question : $\triangle$ABC is an equilateral triangle in which D, E, and F are the points on sides BC, AC, and AB, respectively, such that AD $\perp$ BC, BE $\perp$ AC and CF $\perp$ AB. Which of the following is true?

Option 1: 4AC$^2$ = 5BE$^2$

Option 2: 3AC$^2$ = 4BE$^2$

Option 3: 2AB$^2$ = 3AD$^2$

Option 4: 7AB$^2$ = 9AD$^2$

Question : In $\triangle \mathrm{ABC}$, AB = AC, and D is a point on side AC such that BD = BC. If AB = 12.5 cm and BC = 5 cm, then what is the measure of DC?

Option 1: 2 cm

Option 2: 2.5 cm

Option 3: 3 cm

Option 4: 1.8 cm