Presentation on theme: "Section 12.1: Lines That intersect Circles By: The Balloonicorns."— 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
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 : If a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency : 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 : If two segments are tangent to a circle from the same external point, then the segments are congruent.
How To use Tangents (r + 8) 2 = r Pythagorean Thm. Substitute values c 2 = a 2 + b 2 r r + 64 = r Square of binomial 16r + 64 = 256 r = 12Divide. 16r = 192Subtract 64 from each side Subtract r 2 from each side.
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