Presentation on theme: "Chapter 9.1and 9.2 By: L. Keali’i Alicea"— Presentation transcript:
1Chapter 9.1and 9.2 By: L. Keali’i Alicea Circles TangentsChapter 9.1and 9.2By: L. Keali’i Alicea
2Goals Students will be able… To define a circle, sphere, and terms related to them.Recognize circumscribed circles and inscribed polygons.Apply theorems that relate tangents and radii.Recognize circumscribed polygons and inscribed circles.
3Parts of a CircleCircle FFFcenterUse the center to name a circle.
4Parts of a Circle Segments & Lines chord tangent secant diameter radius
5Radius/diameter radius = ½diameter r = ½ d diameter = 2(radius) FormulasRadius/diameterCircumferenceradius = ½diameterr = ½ ddiameter = 2(radius)d = 2rC = 2∏r or C = ∏d
6Congruent Circles55Two circles are congruent if they have the same radii.
7Concentric circlesCircles that lie in the same plane and have the same center are concentric.
8Inscribed PolygonA polygon is inscribed in a circle if each vertex of the polygon lies on the circle.
9Circumscribed CircleA circle is circumscribed about a polygon if each vertex of the polygon lies on the circle.
10Theorem 9.1If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of tangency.
11Corollary to Theorem 9-1Tangents drawn to a circle from a point are congruent.
12Theorem 9-2If a line in the plane of a circle is perpendicular to a radius at its outer endpoint, then the line is tangent to the circle.
13Common TangentA line that is tangent to each of two coplanar circles is a common tangent.Common internal tangentIntersects the segment joining the centers of the circles. (green line)Common external tangentDoes not intersect the segmentjoining the centers of the circles.(blue line)
14Tangent CirclesTwo coplanar circles that are tangent to the same line at the same point are tangent circles.Internally Tangent Externally Tangent