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Special Segments in a Circle
Transcript of Special Segments in a Circle
Segments of Chords Theorem When two chords intersect inside a circle, each chord is divided into two segments, called chord segments.
If two chords intersect a circle, then the products of the lengths of the chord segments are equal. Segments of Chords Theorem
Example Solve: Segments Intersecting Outside a Circle A secant line is a line that intersects two points in a circle.
A secant segment is a segment of a secant line that has exactly one endpoint on the circle.
A secant that lies in the exterior of the circle is called external secant segment. Theorem 10.16
Secant Segments Theorem If two secants intersect in the exterior of a circle, then the product of the measures of one secant segment and its external secant is equal to the product of the measures of the other secant its external secant segment. Theorem 10.17 If a tangent and a secant intersect in the exterior of the circle, then the square of the measure of the tangent equals the product of the measures of the secant and the external secant segment. Special Segments in a Circle Find measures of segments that intersect the exterior and interior of a circle. K Example: JK2 = JL x JM J L M AC x = AE x AB AD A B C E D A B D C E AB x = BC DB x BE E A D C B D B A C E 0.7 2.5 2.5 AB x BC = DB x BE 2.5 2.5 = 0.7 BE . . 6.25 = 0.7BE 8.9 = BE ANSWER: x