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6.1 Use Properties of Tangents. Vocabulary. A circle is the set of all points in a plane that are equidistant from a given point called the center of the circle. A radius is a segment whose endpoints are the center and any point on the circle. . Vocabulary.

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6.1Use Properties of Tangents


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Vocabulary

  • A circle is the set of all points in a plane that are equidistant from a given point called the center of the circle.

  • A radius is a segment whose endpoints are the center and any point on the circle.


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Vocabulary

  • A chord is a segment whose endpoints are on a circle.

  • A diameter is a chord that contains the center of the circle.

    • The diameter is the longest chord a circle has.


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Vocabulary

  • A secant is a line that intersects a circle in two points.

  • A tangent is a line in the plane of a circle that intersects the circle in exactly one point, the point of tangency.


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Vocabulary

  • Theorem 6.1:

    • In a plane, a line is tangent to a circle if and only if the line is perpendicular to a radius of the circle at its endpoint on the circle.


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Vocabulary

  • Theorem 6.2:

    • Tangent segments from a common external point are congruent.


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Example 1:

  • Tell whether the line, ray, or segment is best described as a radius, chord, diameter, secant, or tangent of circle P.


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Example 2:

  • Use the diagram to find the given lengths.


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Example 3:

  • Tell how many common tangents the circles have and draw them.


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Example 4:

  • RS is tangent to circle C at S and RT is tangent to circle C at T.

    • Find the value of x.


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Example 5:

  • In the diagram, BC is a radius of circle C. Determine whether AB is tangent to circle C. Explain.


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Example 6:

  • In the diagram, B is a point of tangency. Find the radius r of circle C.

**Remember we know that the radius is perpendicular to the tangent**

This makes a RIGHT triangle!

So we can use Pythagorean theorem to solve for r.


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Homework

P. 186 #1, 9-11, 12-20even


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