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 with radii of 25 cm and 9 cm touch each other externally. The length of the direct common tangent is:

Option 1: 34 cm

Option 2: 30 cm

Option 3: 36 cm

Option 4: 32 cm

Question : In two circles centred at O and O’, the distance between the centres of both circles is 17 cm. The points of contact of a direct common tangent between the circles are P and Q. If the radii of both circles are 7 cm and 15 cm, respectively, then the length of PQ is equal to:

Option 1: 15 cm

Option 2: 17 cm

Option 3: 10 cm

Option 4: 22 cm

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