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Geometry Honors Section 9.5 Segments of Tangents, Secants and Chords

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In this section, we will be finding the lengths of segments formed when secants, tangents and/or chords intersect.

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You should already know the following definitions: a tangent is a line in the plane of the circle that intersects a circle in only 1 point a secant is a line that intersects a circle in 2 points a chord is a line segment with endpoints on the circle

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A tangent segment is part of a tangent with one endpoint outside the circle and the second endpoint being the point of tangency.

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A secant segment is part of a secant with one endpoint outside the circle and the second endpoint on the far edge of the circle.

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An external secant segment is part of a secant with one endpoint outside the circle and the second endpoint on the near edge of the circle.

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______ is a tangent (line), ______ is a secant (line), ______ is a tangent segment, ______ is a secant segment, ______ is an external secant segment ______ is a chord.

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Theorem If two secants intersect outside a circle, then the product of the length of one secant segment and its external secant segment equals the product of the other secant segment and its external secant segment. Note: whole x outside = whole x outside

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Theorem If a tangent and a secant intersect outside a circle, then the product of the length of the secant segment and its external secant segment equals the square of the tangent segment.

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Theorem If two chords intersect inside a circle, then the product of the lengths of the two segments on one chord equals the product of the two segments on the second chord.

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Example 4: The piece of pottery shown at the right was found at an archeological site. Determine the diameter of the original piece of pottery. 1.4 in.8 in

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