Chapter 9.1and 9.2 By: L. Keali’i Alicea Circles Tangents Chapter 9.1and 9.2 By: L. Keali’i Alicea

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.

Parts of a Circle Circle F F F center Use the center to name a circle.

Parts of a Circle Segments & Lines chord tangent secant diameter radius

Radius/diameter radius = ½diameter r = ½ d diameter = 2(radius) Formulas Radius/diameter Circumference radius = ½diameter r = ½ d diameter = 2(radius) d = 2r C = 2∏r or C = ∏d

Congruent Circles 5 5 Two circles are congruent if they have the same radii.

Concentric circles Circles that lie in the same plane and have the same center are concentric.

Inscribed Polygon A polygon is inscribed in a circle if each vertex of the polygon lies on the circle.

Circumscribed Circle A circle is circumscribed about a polygon if each vertex of the polygon lies on the circle.

Theorem 9.1 If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of tangency.

Corollary to Theorem 9-1 Tangents drawn to a circle from a point are congruent.

Theorem 9-2 If 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.

Common Tangent A line that is tangent to each of two coplanar circles is a common tangent. Common internal tangent Intersects the segment joining the centers of the circles. (green line) Common external tangent Does not intersect the segment joining the centers of the circles. (blue line)

Tangent Circles Two coplanar circles that are tangent to the same line at the same point are tangent circles. Internally Tangent Externally Tangent

Assignment Finish 9.1 Note Guide problems 1-20.