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Section 12.1: Lines That intersect Circles By: The Balloonicorns.

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Presentation on theme: "Section 12.1: Lines That intersect Circles By: The Balloonicorns."— Presentation transcript:

1 Section 12.1: Lines That intersect Circles By: The Balloonicorns

2 Stuff to learn; Identify tangents, secants, and chords Use properties of tangents to solve problems

3 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

4 Example of the Lines and Segments

5 Examples of Pairs of Circles Concentric Circles Tangent Circles

6 Common Tangent

7 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.

8 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.

9 How To use Tangents (r + 8) 2 = r 2 + 16 2 Pythagorean Thm. Substitute values c 2 = a 2 + b 2 r 2 + 16r + 64 = r 2 + 256 Square of binomial 16r + 64 = 256 r = 12Divide. 16r = 192Subtract 64 from each side Subtract r 2 from each side.

10 Practice

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

12 Practice

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