Section 12.1: Lines That intersect Circles

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Presentation transcript:

Section 12.1: Lines That intersect Circles By: The Balloonicorns

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

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

Example of the Lines and Segments

Examples of Pairs of Circles Concentric Circles Tangent Circles

Common Tangent

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.

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.

How To use Tangents c2 = a2 + b2 Pythagorean Thm. (r + 8)2 = r2 + 162 Substitute values r 2 + 16r + 64 = r2 + 256 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

Practice

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

Practice