Find, to the nearest tenth, the distance between two circles if their radii are 1 and 4 and the

step 1 Question number 20 here we are given that there are two circles there are two circles so they ha

Find, to the nearest tenth, the distance between two circles...

Key Concepts

Circle and Radius

A circle is the set of all points equidistant from a center point, and the radius is the constant distance from this center to any point on the circle. Understanding the role of the radius is fundamental in circle geometry, as it not only defines the size of the circle but also plays a key role in the relationships and formulas involving circles.

Common External Tangent

A common external tangent is a line that touches two circles externally at exactly one point on each circle without crossing the space between them. This concept is important in problems where the relationship between the circles and a tangent line is used to derive distances or establish geometrical relations.

Pythagorean Theorem in Circle Geometry

The Pythagorean theorem is frequently applied in circle geometry to relate the distance between the centers of circles, the difference in their radii, and the length of the tangent line drawn to both circles. In the case of a common external tangent, a right triangle can be formed where one leg represents the difference in the radii and the other leg is the tangent segment, allowing for the calculation of the center-to-center distance.

Distance Between Circles

The distance between two circles typically refers to the shortest distance between their perimeters. When the circles do not intersect, this distance can be calculated by finding the distance between their centers and then subtracting the sum of their radii. This measure is essential when determining how far apart the circles are in a geometric configuration.

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