Question : In a circle, a diameter AB and a chord PQ (which is not a diameter) intersect each other at X perpendicularly. If AX : BX = 3 : 2 and the radius of the circle is 5 cm, then the length of the chord PQ is:

Option 1: $2\sqrt{13}\;\mathrm{cm}$

Option 2: $5\sqrt{3}\;\mathrm{cm}$

Option 3: $4\sqrt{6}\;\mathrm{cm}$ 

Option 4: $6\sqrt{5}\;\mathrm{cm}$

Question : The length of the chord of a circle is 24 cm, and the perpendicular distance between the centre and the chord is 5 cm. The radius of the circle is:

Option 1: 10 cm

Option 2: 13 cm

Option 3: 12 cm

Option 4: 24 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 : 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: $5 \sqrt{ 14} \mathrm{~cm}$

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