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Section 9-2 Tangents

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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.

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Point of Tangency

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

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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.

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Tangent line

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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.

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

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**Common internal tangent**

Intersects the segment joining the centers A B

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**Common external tangent**

Does not intersect the segment joining the centers. A B

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

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Externally Tangent l A B

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Internally Tangent l C D

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Circle. Circle Circle Tangent Theorem 11-1 If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of.

Circle. Circle Circle Tangent Theorem 11-1 If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of.

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