Two circles touch each other. One of the circles has a diameter of 26 cm and the other
circle has a diameter of 12 cm.
Write down
(a) the least distance between the centres of the two circles,
(b) the greatest distance between the centres of the two circles
(a) if the smaller circle is inside the larger circle , the center-to-center distance is ... 7 cm
(b) if the smaller circle is outside the larger circle , the center-to-center distance is ... 19 cm
(a) The least distance between the centers of the two circles can be found by subtracting the radius of the smaller circle from the radius of the larger circle. In this case, the radius of the larger circle is half of its diameter, so it is 26 cm/2 = 13 cm. The radius of the smaller circle is 12 cm/2 = 6 cm. Therefore, the least distance between the centers is 13 cm - 6 cm = 7 cm.
(b) The greatest distance between the centers of the two circles is the sum of the radii of the circles. So, in this case, it would be 13 cm + 6 cm = 19 cm.
To find the least and greatest distances between the centers of the two circles, we can use the following formulas:
(a) The least distance between the centers of the circles is equal to the difference between the radii of the circles:
Least Distance = Radius of Circle 1 - Radius of Circle 2
(b) The greatest distance between the centers of the circles is equal to the sum of the radii of the circles:
Greatest Distance = Radius of Circle 1 + Radius of Circle 2
Given the diameters of the circles, we can calculate the radii as follows:
Radius of Circle 1 = Diameter of Circle 1 / 2 = 26 cm / 2 = 13 cm
Radius of Circle 2 = Diameter of Circle 2 / 2 = 12 cm / 2 = 6 cm
Now we can substitute the values into the formulas:
(a) Least Distance = 13 cm - 6 cm = 7 cm
(b) Greatest Distance = 13 cm + 6 cm = 19 cm
So,
(a) The least distance between the centers of the two circles is 7 cm.
(b) The greatest distance between the centers of the two circles is 19 cm.
To find the least distance between the centers of the two circles, you can subtract the radius of the smaller circle from the radius of the larger circle.
(a) The smaller circle has a diameter of 12 cm, which means its radius is half of its diameter, so the radius of the smaller circle is 12 cm / 2 = 6 cm. The larger circle has a diameter of 26 cm, so its radius is 26 cm / 2 = 13 cm. Therefore, the least distance between the centers of the two circles is 13 cm - 6 cm = 7 cm.
To find the greatest distance between the centers of the two circles, you can add the radius of the smaller circle to the radius of the larger circle.
(b) Using the same radii as before, the greatest distance between the centers of the two circles is 13 cm + 6 cm = 19 cm.
So, the answers are:
(a) The least distance between the centers of the two circles is 7 cm.
(b) The greatest distance between the centers of the two circles is 19 cm.