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10.1 Use Properties of Tangents

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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

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

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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

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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

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

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

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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

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Tangent Circles Externally Internally

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Common Internal Tangent Common External Tangent

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

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

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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

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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

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

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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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Chapter 14: CIRCLES!!! Proof Geometry.

Chapter 14: CIRCLES!!! Proof Geometry.

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