Presentation on theme: "Chapter 9.1and 9.2 By: L. Keali’i Alicea"— Presentation transcript:
1 Chapter 9.1and 9.2 By: L. Keali’i Alicea Circles TangentsChapter 9.1and 9.2By: L. Keali’i Alicea
2 Goals 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.
3 Parts of a CircleCircle FFFcenterUse the center to name a circle.
4 Parts of a Circle Segments & Lines chord tangent secant diameter radius
5 Radius/diameter radius = ½diameter r = ½ d diameter = 2(radius) FormulasRadius/diameterCircumferenceradius = ½diameterr = ½ ddiameter = 2(radius)d = 2rC = 2∏r or C = ∏d
6 Congruent Circles55Two circles are congruent if they have the same radii.
7 Concentric circlesCircles that lie in the same plane and have the same center are concentric.
8 Inscribed PolygonA polygon is inscribed in a circle if each vertex of the polygon lies on the circle.
9 Circumscribed CircleA circle is circumscribed about a polygon if each vertex of the polygon lies on the circle.
10 Theorem 9.1If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of tangency.
11 Corollary to Theorem 9-1Tangents drawn to a circle from a point are congruent.
12 Theorem 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.
13 Common 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)
14 Tangent CirclesTwo coplanar circles that are tangent to the same line at the same point are tangent circles.Internally Tangent Externally Tangent