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Tangents to Circles Pg 595

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Circle the set of all points equidistant from a given point ▫Center Congruent Circles ▫have the same radius “Circle P” or ○ P

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Radius, r the distance from the center to a point on the circle a segment whose endpoints are the center of the circle and a point on the circle all radii of a circle are congruent

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Diameter, d the distance across the circle, through the center a chord that passes through the center of the circle twice the radius (r), so d = 2r

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Segments in a circle Chord ▫a segment whose endpoints are on the circle Secant ▫a line that intersects a circle in two points Tangent ▫a line in the plane of a circle that intersects the circle in exactly one point ▫Point of tangency – where the line intersects the circle

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Name the segments Diameter ▫AD Radius ▫AC or CD Tangent ▫EG Chord ▫BH

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Intersection of Circles 2 points 1 point ▫Internally tangent ▫Externally tangent None ▫Concentric

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Internal Tangents

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External Tangents

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Theorem 10.1 If a line is tangent to a circle, then it is perpendicular to the radius drawn from the point of tangency.

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Theorem 10.2 In a plane, if a line is perpendicular to a radius of a circle at its endpoint on the circle, then the line is tangent to the circle.

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Is EF tangent to Circle D? 10.2 - EF is a tangent if EF ┴ DE Converse of the Pythagorean theorem: 11 2 + 60 2 = 61 2 3721 = 3721 DEF Right Triangle EF ┴ DE thus EF is a tangent

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Theorem 10.3 If two segments from the same exterior point are tangent to a circle, then they are congruent.

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Find x Because segment AB and BC are external tangents, they are congruent. So: 4x-9=2x+5 2x = 14 x = 7

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Properties of Tangents. EXAMPLE 1 Identify special segments and lines Tell whether the line, ray, or segment is best described as a radius, chord, diameter,

Properties of Tangents. EXAMPLE 1 Identify special segments and lines Tell whether the line, ray, or segment is best described as a radius, chord, diameter,

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