Unit 6-2 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.

Lines that Intersect Circles Chord Secant Tangent A line segment whose endpoints are on the edge of the circle. A line that intersects a circle at two points. A line that intersects a circle at one point.

Lines that Intersect Circles Concentric Circles Congruent Circles Circles that share a common center point Circles that have equal radii Two circles that intersect at one point Tangent Circles

Lines that Intersect Circles Chord Secant Tangent

Identify each line or segment that intersects  L. Example 1 Chord Diameter Radii Secant Tangent

Lines that Intersect Circles Congruent Circles 5 5 Concentric Circles Tangent Circles

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  R: radius of  S: Point of Tangency: Equation of the tangent line:

Example 3 Find the length of each radius. Identify the point of tangency and write the equation of the tangent line at this point. radius of  D: radius of  C: Point of Tangency: Equation of the Tangent line:

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

Example 4 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? The distance from the center of the earth to the horizon is 4000 mi.

Example 5 HK and HG are tangent to  F. Find HG.

RS and RT are tangent to  Q. Find RS. Example 6