11.1.1 Lines That Intersect Circles
Key Objectives • Identify tangents, secants, and chords. • Use properties of tangents to solve problems. Key Terms
• 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. • A chord is a segment whose endpoints lie on a circle. • A secant is a line that intersects a circle at two points.
• A tangent is a line in the same plane as a circle that intersects it at exactly one point. • The point where the tangent and a circle intersect is called the point of tangency . • Two circles are congruent circles if and only if they have congruent radii. • Concentric circles are coplanar circles with the same center. • Two coplanar circles that intersect at exactly one point are called tangent circles . • A common tangent is a line that is tangent to two circles. Theorems, Postulates, Corollaries, and Properties • Theorem If a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency. • Theorem If a line is perpendicular to a radius of a circle at a point on the circle, then the line is tangent to the circle. • Theorem If two segments are tangent to a circle from the same external point, then the segments are congruent. Example 1 Identifying Lines and Segments that Intersect Circles
A chord is a line segment that has its endpoints on a circle. EF is an example of a chord, and the segment CD is also a chord. A secant is a line that intersects a circle at two points. Line CD is an example of a secant. A tangent is a line that intersects a circle at one point. A tangent is in the plane of a circle. Line m is an example of a tangent. The point of intersection with the circle of a tangent is the point of tangency. The point of tangency for line m is G . A radius is a segment that extends from the center of the circle to a point on the circle. A diameter is a chord that passes through the center of a circle.
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