# 10.1 Use Properties of Tangents.  Circle - the set of all points in a plane that are equidistant from a given point.  Center - point in the middle of.

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10.1 Use Properties of Tangents

 Circle - the set of all points in a plane that are equidistant from a given point.  Center - point in the middle of the circle  Radius - distance from the center of a circle to a point on the circle  Diameter - a chord that passes through the center of a circle. Definitions

P P is the center of the circle Q R QR is a diameter S QP, PR, and PS are radii

 Chord - a segment whose end points are on the circle.  Secant - a line that intersects a circle at 2 points (the line containing a chord)  Tangent - a line that intersects a circle in exactly one point.  Point of Tangency – the point where a tangent intersects the circle More Definitions

A B C D E l AC is a chord Line l is a tangent ED is a secant B is the point of tangency

 AH  EI  DF  CE A B C D E F G H I tangent diameter chord radius

 Concentric Circles circles that have a common center but different radii lengths More Definitions

 Tangent Circles - circles that intersect at one point  Common Tangent - a line or segment that is tangent to two circles  Common Internal Tangent - a tangent that intersects the segment that connects the centers of the circles  Common External Tangent - does not intersect the segment that connects the centers

Tangent Circles Externally Internally

Common Internal Tangent Common External Tangent

example Is the segment common internal or external tangent? Common Internal

Tangent/Radius Theorem  If a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency.

example Is CE tangent to circle D? Explain D E C 11 45 43 11 2 + 43 2 = 45 2 121 + 1849 = 2025 1970 = 2025 NO

example Solve for the radius, r A B C r 28ft 14ft r 2 + 28 2 = (r + 14) 2 r 2 + 784 = r 2 + 28r + 196 784 = 28r + 196 588 = 28r 21 = r

Congruent Tangents Corollary  If 2 segments from the same exterior point are tangent to a circle, then they are .

example AB is tangent to circle C at point B. AD is tangent to circle C at point D. Find the value of x. C B D A x 2 + 8 44 x 2 + 8 = 44 x 2 = 36 x = 6

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