Question : Two circles with their centres at O and P and radii 8 cm and 4 cm respectively touch each other externally. The length of their common tangent is:

Option 1: 8.5 cm

Option 2: $\frac{8}{\sqrt{2}}$ cm

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

Option 4: 8 cm

Question : Two circles of radii 5 cm and 3 cm intersect each other at A and B, and the distance between their centres is 6 cm. The length (in cm) of the common chord AB is:

Option 1: $\frac{4 \sqrt{13}}{3}$

Option 2: $\frac{2 \sqrt{14}}{3}$

Option 3: $\frac{2 \sqrt{13}}{3}$

Option 4: $\frac{4 \sqrt{14}}{3}$

Question : What is the length (in cm) of the transverse common tangent between two circles with radii 6 cm and 4 cm, given that the distance between their centres is 14 cm?

Option 1: $2 \sqrt{6}$

Option 2: $4 \sqrt{6}$

Option 3: $5 \sqrt{6}$

Option 4: $3 \sqrt{6}$

Question : Out of two concentric circles, the radius of the outer circle is 6 cm and the chord PQ of the length 10 cm is a tangent to the inner circle. Find the radius (in cm) of the inner circle.

Option 1: $4$

Option 2: $\sqrt{7}$

Option 3: $\sqrt{13}$

Option 4: $\sqrt{11}$

Question : Two circles of radii 8 cm and 3 cm, respectively, are 13 cm apart. AB is a direct common tangent touch to both the circles at A and B respectively then the length of AB is:

Option 1: 10 cm

Option 2: 12 cm

Option 3: 8 cm

Option 4: 6 cm