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12.1 Tangent Lines

12.1 Tangent Lines. A tangent to a circle is a line in the plane of the circle that intersects the circle in exactly one point. The point where a circle and a tangent intersect is the point of tangency. Theorem 12.1.

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12.1 Tangent Lines

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  1. 12.1 Tangent Lines • A tangent to a circle is a line in the plane of the circle that intersects the circle in exactly one point. • The point where a circle and a tangent intersect is the point of tangency.

  2. Theorem 12.1 • If a line is tangent to a circle, then the line is perpendicular to the radius at the point of tangency.

  3. Finding Angle Measures • Segment ML and segment MN are tangent to circle O. What is the value of x? LMNO is a quadrilateral. The sum of the angles is 360. 90 + 117 + 90 + x = 360 297 + x = 360 x = 63 The measure of angle M is 63°.

  4. Theorem 12.2 • If a line in the plane of a circle is perpendicular to a radius at its endpoint on the circle, then the line is tangent to the circle.

  5. Finding a Radius • What is the radius of circle C?

  6. Identifying a Tangent • Is segment ML tangent to circle N at L? Explain.

  7. Theorem 12.3 • If two tangent segments to a circle share a common endpoint outside the circle, then the two segments are congruent.

  8. More Practice!!!!! • Homework – Textbook p. 767 # 6 – 17.

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