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Unformatted text preview: 141/142 Circles and Spheres/Tangent Lines to Circles A)
a. Basic Definitions Circle with center P and radius r i. The set of all points of the plane whose distance from P is equal to r b. Sphere with center P and radius r i. The set of all points of space whose distance from P is equal to r c. Chord i. A segment whose endpoints are on the circle d. Secant i. A line which intersects the circle in two points e. Diameter i. A chord containing the center f. Radius i. Is a segment from the center to a point of the circle ii. Two meanings of radius 1. A segment 2. A number g. Great circle i. The intersection of a sphere with a plane through its center B)
a. Example Name a chord/radius/diameter/secant b. C)
a. Theorem 141 The intersection of a sphere with a plane through its center is a circle with the same center and the same radius D)
a. 142 Tangent Lines to Circles Interior of a circle i. Points whose distance from the center is less than the radius b. Exterior of a circle i. Points whose distance from the center is greater than the radius c. Tangent i. A line (in the same plane) which intersects the circle in one and only one point d. Concentric i. Two or more coplanar circles or two or more spheres with the same center E) Theorem 142 a. A line perpendicular to a radius at its outer end is tangent to the circle b. F)
a. Theorem 143 Every tangent to a circle is perpendicular to the radius drawn to the point of contact G)
a. Definition Tangent i. Two circles are tangent if they are tangent to the same line at the same point b. Internally tangent i. When two tangent circles are coplanar and their centers are on the same side of their common tangent c. Externally tangent i. When two tangent circles are coplanar and their centers are on opposite sides of their common tangent H)
a. Example (4 from the hw) Given two concentric circles, every chord of the greater circle which is tangent to the smaller circle is bisected at its point of tangency statement 1) reason 1) Given 2) 3) 4) 2) 3) 4) ...
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This note was uploaded on 05/16/2011 for the course ALGEBRA 098 taught by Professor Johnson during the Spring '09 term at Grand Valley State University.
 Spring '09
 Johnson
 Algebra

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