Question : The length of the common chord of two intersecting circles is 12 cm. If the diameters of the circles are 15 cm and 13 cm, then what is the distance (in cm) between their centres?

Option 1: $\frac{7}{2}$

Option 2: $7$

Option 3: $7\sqrt{2}$

Option 4: $14$

Question : 8 cm and 5 cm are the radii of two circles. If the distance between the centres of the two circles is 11 cm, then the length (in cm) of the common tangent of the two circles is:

Option 1: $2 \sqrt{7}$

Option 2: $3 \sqrt{7}$

Option 3: $\sqrt{7}$

Option 4: $4\sqrt{7}$

Question : If the radii of two circles are 7 cm and 4 cm and the length of the transverse common tangent is 13 cm, then the distance between the two centres is:

Option 1: $\sqrt{290}$ cm

Option 2: $\sqrt{190}$ cm

Option 3: $\sqrt{128}$ cm

Option 4: $\sqrt{240}$ cm

Question : The radii of the two circles are 9 cm and 4 cm, the distance between their centres is 13 cm, then the length of the direct common tangent is:

Option 1: 8 cm

Option 2: 14 cm

Option 3: 12 cm

Option 4: 16 cm

Question : The radii of the two circles are 11 cm and 3 cm. The distance between their centres is 17 cm. What is the length of the direct common tangent?

Option 1: 12 cm

Option 2: 14 cm

Option 3: 16 cm

Option 4: 15 cm

Question : The distance between the centres of two circles having radii of 24 cm and 18 cm, respectively, is 48 cm. Find the length (in cm) of a direct common tangent to the two circles.

Option 1: $20 \sqrt{6}$

Option 2: $18 \sqrt{7}$

Option 3: $45$

Option 4: $22 \sqrt{5}$