Presentation on theme: "Section 12.1: Lines That intersect Circles"— 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 circleExterior of a Circle – The set of all points outside the circleChord – A segment whose endpoints lie on a circleSecant – A line that intersects a circle at two pointsTangent of a Circle – A line in the same plane as a circle that intersects it at exactly one pointPoint of Tangency – The point where the tangent and circle intersectCongruent Circles – Two circles that have congruent radiiConcentric Circles – Coplanar circles with the same centerTangent Circles – Two coplanar circles that intersect at exactly one pointCommon Tangent – A line that is tangent to two circles
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 THEOREMS12-1-1: 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 c2 = a2 + b2 Pythagorean Thm. (r + 8)2 = r2 + 162 Substitute valuesr r + 64 = rSquare of binomial16r + 64 = 256Subtract r2 from each side.16r = 192Subtract 64 from each sider = 12Divide.How To use Tangents
11 Using Properties of Tangents AB = ADTwo tangent segments from the same point are 11 = x2 + 2Substitute values9 = x2Subtract 2 from each side.3 = xFind the square root of 9.Using Properties of Tangents