The image contains three diagrams illustrating the relative positions of two circles. The diagrams label the radii of the circles as R and r, and the distance between their centers as d. The text above the diagrams, "На рисунках показаны взаимные расположения двух окружностей.", translates to "The figures show the relative positions of two circles.". The task is to analyze these configurations.

Analysis of Circle Positions

The provided image displays three scenarios depicting the relationship between two circles. Each scenario involves two circles with radii labeled R and r, and the distance between their centers labeled d.

Scenario 1: External Tangency

• In the first diagram, the two circles are positioned such that they touch each other at exactly one point on the outside.
• This configuration occurs when the distance between the centers (d) is equal to the sum of their radii (R + r).
• Visually, d = R + r.

Scenario 2: Intersecting Circles

• The second diagram shows two circles that intersect at two distinct points.
• This occurs when the distance between the centers (d) is less than the sum of their radii (R + r) but greater than the absolute difference of their radii (|R - r|).
• Visually, |R - r| < d < R + r.

Scenario 3: Internal Tangency

• The third diagram illustrates two circles where one circle is inside the other, and they touch at exactly one point.
• This configuration occurs when the distance between the centers (d) is equal to the absolute difference of their radii (|R - r|). Assuming R > r, then d = R - r.
• Visually, d = |R - r|.

These three scenarios cover the fundamental ways two circles can be positioned relative to each other in a plane.