Question : What is the perimeter of a square inscribed in a circle of radius 5 cm?

Option 1: $20 \sqrt{2}\ \mathrm{~cm}$

Option 2: $40\sqrt{2}\ \mathrm{~cm}$

Option 3: $30\sqrt{2}\ \mathrm{~cm}$

Option 4: $10\sqrt{2}\ \mathrm{~cm}$

Question : Two circles touch each other externally. The radius of the first circle with centre O is 12 cm. Radius of the second circle with centre A is 8 cm. Find the length of their common tangent BC.

Option 1: $6 \sqrt{6} \mathrm{~cm}$

Option 2: $8 \sqrt{3} \mathrm{~cm}$

Option 3: $8 \sqrt{2} \mathrm{~cm}$

Option 4: $8 \sqrt{6} \mathrm{~cm}$

Question : In an equilateral triangle of side 24 cm, a circle is inscribed touching its sides. The area of the remaining portion of the triangle is:

Option 1: $98.55\;\mathrm{cm^2}$

Option 2: $100 \;\mathrm{cm^2}$

Option 3: $101 \;\mathrm{cm^2}$

Option 4: $95\;\mathrm{cm^2}$

Question : The radius of a circle with centre at O is 6 cm and the central angle of a sector is 40°. Find the area of the sector.

Option 1: $6 \pi ~\mathrm{cm}^2$

Option 2: $5 \pi ~\mathrm{cm}^2$

Option 3: $4 \pi ~\mathrm{cm}^2$

Option 4: $8 \pi ~\mathrm{cm}^2$

Question : The area of a sector of a circle is 88 sq. cm., and the angle of the sector is 45°. Find the radius of the circle. (Use $\pi=\frac{22}{7}$)

Option 1: $3 \sqrt{ 11} \mathrm{~cm}$

Option 2: $4 \sqrt{ 14} \mathrm{~cm}$

Option 3: $6 \sqrt{ 13} \mathrm{~cm}$

Option 4: $5 \sqrt{ 14} \mathrm{~cm}$