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**Section 12.1: Lines That intersect Circles**

By: The Balloonicorns

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**Stuff to learn; Identify tangents, secants, and chords**

Use properties of tangents to solve problems

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**Words and Phrases to Remember**

Interior of a Circle – The set of all points inside the circle Exterior of a Circle – The set of all points outside the circle Chord – A segment whose endpoints lie on a circle Secant – A line that intersects a circle at two points Tangent of a Circle – A line in the same plane as a circle that intersects it at exactly one point Point of Tangency – The point where the tangent and circle intersect Congruent Circles – Two circles that have congruent radii Concentric Circles – Coplanar circles with the same center Tangent Circles – Two coplanar circles that intersect at exactly one point Common Tangent – A line that is tangent to two circles

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**Example of the Lines and Segments**

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**Examples of Pairs of Circles**

Concentric Circles Tangent Circles

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Common Tangent

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**How to Identify Tangents of Circles**

Center of circle A is (4, 4), and its radius is 4. The center of circle B is (5, 4) and its radius is 3. The two circles have one point of intersection (8, 4). The vertical line x = 8 is the only common tangent of the two circles.

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THEOREMS 12-1-1: If a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency. 12-1-2: If a line is perpendicular to a radius of a circle at a point on the circle, then the line is tangent to the circle. 12-1-3: If two segments are tangent to a circle from the same external point, then the segments are congruent.

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**How To use Tangents c2 = a2 + b2 Pythagorean Thm. (r + 8)2 = r2 + 162**

Substitute values r r + 64 = r Square of binomial 16r + 64 = 256 Subtract r2 from each side. 16r = 192 Subtract 64 from each side r = 12 Divide. How To use Tangents

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Practice

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**Using Properties of Tangents**

AB = AD Two tangent segments from the same point are 11 = x2 + 2 Substitute values 9 = x2 Subtract 2 from each side. 3 = x Find the square root of 9. Using Properties of Tangents

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Practice

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Lines that intersect Circles

Lines that intersect Circles

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