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Understanding Circles: Interior, Exterior, and Tangent

This photograph taken from space highlights the curvature of the Earth's horizon. Learn about the vocabulary of circles and how it relates to Earth. Identify lines and segments that intersect circles, find the length of radii and equation of tangent lines, solve real-world problems, and understand the concept of common tangents.

margaretbaldridge
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Understanding Circles: Interior, Exterior, and Tangent

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  1. 10.1 Vocabulary interior of a circle concentric circles exterior of a circle tangent circles chord common tangent secant tangent of a circle point of tangency congruent circles

  2. This photograph was taken 216 miles above Earth. From this altitude, it is easy to see the curvature of the horizon. Facts about circles can help us understand details about Earth. Recall that a circle is the set of all points in a plane that are equidistant from a given point, called the center of the circle. A circle with center C is called circle C, or C. The interior of a circleis the set of all points inside the circle. The exterior of a circleis the set of all points outside the circle.

  3. Example 1: Identifying Lines and Segments That Intersect Circles Identify each line or segment that intersects L. chords: secant: tangent: diameter: radii:

  4. Example 2: Identifying Tangents of Circles Find the length of each radius. Identify the point of tangency and write the equation of the tangent line at this point. radius of R: 2 radius of S: 1.5 point of tangency: (–2, 0) equation of tangent line: y = 0

  5. A common tangent is a line that is tangent to two circles.

  6. Example 3: Problem Solving Application Early in its flight, the Apollo 11 spacecraft orbited Earth at an altitude of 120 miles. What was the distance from the spacecraft to Earth’s horizon rounded to the nearest mile? (use rearth = 4000mi) Kilimanjaro, the tallest mountain in Africa, is 19,340 ft tall. What is the distance from the summit of Kilimanjaro to the horizon to the nearest mile?

  7. HK and HG are tangent to F. Find HG. Example 4: Using Properties of Tangents

  8. 3. FE and FG are tangent to F. Find FG. Lesson Quiz: Part III 1. Identify each line or segment that intersects Q. 2. Mount Mitchell peaks at 6,684 feet. What is the distance from this peak to the horizon, rounded to the nearest mile? 90

  9. Common Tangent Procedure • Draw the segment to connect the centers of the circles • Draw the radii to the points of tangency (they should be parallel) • Through the center of the smaller circle, draw a line parallel to the common tangent • Notice that this line intersects the radius of the larger circle, extended if necessary, to form a right triangle. • Solve the problem using right triangle properties. Common Tangent Examples…

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