Question : Two circles with diameters of 50 cm and 58 cm, respectively, intersect each other at points A and B, such that the length of the common chord is 40 cm. Find the distance (in cm) between the centres of these two circles.

Option 1: 34

Option 2: 37

Option 3: 36

Option 4: 35

Question : Two circles of radius 2.4 cm and 4 cm, respectively, have a common tangent. The distance between the centres of the two circles is 6.5 cm. If the common tangent does not intersect the line joining the centres, then find the length of a common tangent to the circles.

Option 1: 6.0 cm

Option 2: 6.2 cm

Option 3: 6.1 cm

Option 4: 6.3 cm

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 : The Radii of the two circles are 20 cm and 4 cm. Length of the direct common tangent is 30 cm. What is the distance between their centres?

Option 1: 36 cm

Option 2: 38 cm

Option 3: 34 cm

Option 4: 32 cm

Question : Find the distance (in cm) between the centres of two circles having radii of 32 cm and 24 cm, respectively if the length of a direct common tangent to the two circles is given as 24 cm.

Option 1: 60

Option 2: 65

Option 3: 64

Option 4: 63

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: $22 \sqrt{5}$