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Secants and Tangents

Secants and Tangents. A secant to a circle is a line that intersects the circle at two points. Secants and Tangents. A tangent is a line in the plane of the circle that intersects the circle at exactly one point. This point is the point of tangency. Tangent Theorem.

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Secants and Tangents

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  1. Secants and Tangents • A secant to a circle is a line that intersects the circle at two points.

  2. Secants and Tangents • A tangent is a line in the plane of the circle that intersects the circle at exactly one point. • This point is the point of tangency.

  3. Tangent Theorem • If a line is tangent to a circle, then the line is perpendicular to a radius of the circle drawn to the point of tangency.

  4. Radius and Chord Theorem • A radius that is perpendicular to a chord of a circle bisects the chord.

  5. Converse of the Tangent Theorem • If a line is perpendicular to a radius of a circle at its endpoint on the circle, then the line is tangent to the circle.

  6. Additional Theorem • The perpendicular bisector of a chord passes through the center of the circle.

  7. EXAMPLES • Refer to the diagram below. List all congruent segments.

  8. EXAMPLES • 2. DC = 4. Find BD.

  9. EXAMPLES • 3. The circle has a radius of 13. AD is 5 and • Find CB.

  10. EXAMPLES • 4. Verify that is tangent to at H.

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