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,
....................................................... cm
(b) the greatest distance between the centres of the two circles
draw the two circles, and a line through their centers.
Label the radii, and it should be clear what the two distances are.
To find the least and greatest distances between the centers of the two circles, we can use the properties of tangent lines and circles.
First, let's define the centers of the circles as C1 and C2. The diameter of the first circle is 26 cm, so the radius is half of that, which is 13 cm (r1 = 13 cm). The diameter of the second circle is 12 cm, so the radius is half of that, which is 6 cm (r2 = 6 cm).
(a) To find the least distance between the centers of the two circles, we consider the case where the circles are tangent to each other. In this case, the distance between the centers is the sum of the radii of the two circles.
So, the least distance between the centers is:
d1 = r1 + r2
d1 = 13 cm + 6 cm
d1 = 19 cm
Therefore, the least distance between the centers of the two circles is 19 cm.
(b) To find the greatest distance between the centers of the two circles, we consider the case where both circles are positioned to be tangent externally to a straight line.
In this case, the centers of the two circles and the point of tangency form a line where the distance between the centers is the difference between the radii of the two circles.
So, the greatest distance between the centers is:
d2 = r1 - r2
d2 = 13 cm - 6 cm
d2 = 7 cm
Therefore, the greatest distance between the centers of the two circles is 7 cm.