Question : In the given figure, B and C are the centres of the two circles. ADE is the common tangent to the two circles. If the ratio of the radii of both circles is 3 : 5 and AC is 40 cm, then what is the value (in cm) of DE?

Option 1: $3\sqrt{15}$

Option 2: $5\sqrt{15}$

Option 3: $6\sqrt{15}$

Option 4: $4\sqrt{15}$

Question : The distance between the centres of two circles having radii 16 cm and 8 cm, is 26 cm. The length (in cm) of the direct common tangent of the two circles is:

Option 1: $2 \sqrt{132}$

Option 2: $\sqrt{153}$

Option 3: $2 \sqrt{153}$

Option 4: $\sqrt{132}$

Question : The distance between the centres of two circles having radii 22 cm and 18 cm, is 32 cm. The length (in cm) of the direct common tangent of the two circles is:

Option 1: $2 \sqrt{252} \mathrm{~cm}$

Option 2: $2 \sqrt{152} \mathrm{~cm}$

Option 3: $3 \sqrt{242} \mathrm{~cm}$

Option 4: $3 \sqrt{252} \mathrm{~cm}$

Question : The distance between the centres of two circles having radii of 8 cm and 3 cm is 13 cm. The length (in cm) of the direct common tangent of the two circles is:

Option 1: 15 cm

Option 2: 16 cm

Option 3: 18 cm

Option 4: 12 cm

Question : If the radii of two circles are 6 cm and 3 cm and the length of the transverse common tangent is 8 cm, then the distance between the two centres is:

Option 1: $\sqrt{145} \text{ cm}$

Option 2: $\sqrt{140} \text{ cm}$

Option 3: $\sqrt{150} \text{ cm}$

Option 4: $\sqrt{135} \text{ cm}$

Question : The radius of two circles is 3 cm and 4 cm. The distance between the centres of the circles is 10 cm. What is the ratio of the length of the direct common tangent to the length of the transverse common tangent?

Option 1: $\sqrt{51}:\sqrt{68}$

Option 2: $\sqrt{33}:\sqrt{17}$

Option 3: $\sqrt{66}:\sqrt{51}$

Option 4: $\sqrt{28}:\sqrt{17}$