12 1 Lines That Intersect Circles Vocabulary interior

12 -1 Lines That Intersect Circles Vocabulary interior of a circle exterior of a circle chord secant tangent of a circle point of tangency congruent circles Holt Mc. Dougal Geometry concentric circles tangent circles common tangent

12 -1 Lines That Intersect Circles 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. Holt Mc. Dougal Geometry

12 -1 Lines That Intersect Circles The interior of a circle is the set of all points inside the circle. The exterior of a circle is the set of all points outside the circle. Holt Mc. Dougal Geometry

12 -1 Lines That Intersect Circles Holt Mc. Dougal Geometry

12 -1 Lines That Intersect Circles Check It Out! Example 1 Identify each line or segment that intersects P. chords: QR and ST secant: ST tangent: UV diameter: ST radii: PQ, PT, and PS Holt Mc. Dougal Geometry

12 -1 Lines That Intersect Circles Holt Mc. Dougal Geometry

12 -1 Lines That Intersect Circles Check It Out! Example 2 Find the length of each radius. Identify the point of tangency and write the equation of the tangent line at this point. radius of C: 1 Center is (2, – 2). Point on is (2, – 1). Distance between the 2 points is 1. radius of D: 3 Center is (2, 2). Point on is (2, – 1). Distance between the 2 points is 3. Holt Mc. Dougal Geometry

12 -1 Lines That Intersect Circles Check It Out! Example 2 Continued Find the length of each radius. Identify the point of tangency and write the equation of the tangent line at this point. Pt. of tangency: (2, – 1) Point where the s and tangent line intersect eqn. of tangent line: y = – 1 Horizontal line through (2, -1) Holt Mc. Dougal Geometry

12 -1 Lines That Intersect Circles A common tangent is a line that is tangent to two circles. Holt Mc. Dougal Geometry

12 -1 Lines That Intersect Circles A common tangent is a line that is tangent to two circles. Holt Mc. Dougal Geometry

12 -1 Lines That Intersect Circles Holt Mc. Dougal Geometry

12 -1 Lines That Intersect Circles 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? Holt Mc. Dougal Geometry

12 -1 Lines That Intersect Circles Holt Mc. Dougal Geometry

12 -1 Lines That Intersect Circles Check It Out! Example 4 a RS and RT are tangent to Q. Find RS. Holt Mc. Dougal Geometry

12 -1 Lines That Intersect Circles Lesson Quiz: Part I 1. Identify each line or segment that intersects Q. chords VT and WR secant: VT tangent: s diam. : WR radii: QW and QR Holt Mc. Dougal Geometry

12 -1 Lines That Intersect Circles Lesson Quiz: Part II 2. Find the length of each radius. Identify the point of tangency and write the equation of the tangent line at this point. radius of C: 3 radius of D: 2 pt. of tangency: (3, 2) eqn. of tangent line: x = 3 Holt Mc. Dougal Geometry

12 -1 Lines That Intersect Circles Lesson Quiz: Part III 3. Mount Mitchell peaks at 6, 684 feet. What is the distance from this peak to the horizon, rounded to the nearest mile? 101 mi 4. FE and FG are tangent to F. Find FG. 90 Holt Mc. Dougal Geometry