Question : In $\triangle$PQR, $\angle$ PQR = $90^{\circ}$, PQ = 5 cm and QR = 12 cm. What is the radius (in cm) of the circumcircle of $\triangle$PQR?

Option 1: 6.5

Option 2: 7.5

Option 3: 13

Option 4: 15

Question : The area of an equilateral triangle is $4 \sqrt{3} \mathrm{~cm}^2$. Find the side (in cm) of the triangle.

Option 1: $2$

Option 2: $4$

Option 3: $\sqrt{3}$

Option 4: $2 \sqrt{3}$

Question : If each side of an equilateral triangle is 12 cm, then its altitude is equal to:

Option 1: $6 \sqrt{3}\ \text{cm}$

Option 2: $3 \sqrt{6}\ \text{cm}$

Option 3: $6 \sqrt{2}\ \text{cm}$

Option 4: $3 \sqrt{2}\ \text{cm}$

Question : $\triangle$ PQR circumscribes a circle with centre O and radius r cm such that $\angle$ PQR = $90^{\circ}$. If PQ = 3 cm, QR = 4 cm, then the value of r is:

Option 1: 2

Option 2: 1.5

Option 3: 2.5

Option 4: 1

Question : The length of each side of an equilateral triangle is $14 \sqrt{3}$ cm. The area of the incircle (in cm²), is:

Option 1: 450

Option 2: 308

Option 3: 154

Option 4: 77