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Section 9-2

Learn the theorems and properties related to tangents of circles, including perpendicularity, congruence, circumscribed polygons, and common tangent configurations. Understand the concepts of external and internal tangents and tangent circles alignments.

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Section 9-2

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  1. Section 9-2 Tangents

  2. Theorem 9-1 • If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of tangency.

  3. Point of Tangency

  4. P Corollary • Tangents to a circle from a common point are congruent A B

  5. Theorem 9-2 • If a line in the plane of a circle is perpendicular to the radius at its outer endpoint, then the line is tangent to the circle.

  6. Tangent line

  7. When each side of a polygon is tangent to a circle, the polygon is said to be circumscribed about the circle and the circle is inscribed in the polygon.

  8. Common tangent • A line that is tangent to each of two coplanar circles

  9. A B Common internal tangent • Intersects the segment joining the centers

  10. B A Common external tangent • Does not intersect the segment joining the centers.

  11. Tangent circles • Coplanar circles that are tangent to the same line at the same point

  12. Externally Tangent l A B

  13. Internally Tangent l D C

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