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Bellwork 1) (x+3)(x+7) 2) (2x+4)(x-4)

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10.5 Segment Lengths in Circles

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Segments of Chord Theorem If two chords intersect in the interior of a circle,then the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord. D A C B E EA EB = EC ED *We can set up a proportion to find the missing length!

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D A C B E x

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D A C B E Example a) x

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D A C B E 8 9 2x x

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D A C B E x+1 x

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D A C B E x+5 x+3 x+2 Example e)

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external secant segment tangent segment secant segment touches 2 places touches 1 place When two chords intersect in a circle, each chord is divided into two segment called segments of the chord. A secant segment is a segment that contains a chord of a circle, and exactly one endpoint outside the circle. The part of the secant that is outside of the circle is called an external segment.

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Segments of Secants Theorem If two secant segments share the same endpoint outside a circle, then the product of the lengths of one secant segment and its external segment equals the product of the lengths of the other secant segment and its external segment. E A B C D EA EB = EC ED

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E A B C D 11 9 x 10

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E A B C D 4 4 x 2 Example b)

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You try b) E A B C D 8 6 x 7

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E A B C D Example b)

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E A B C D x+3 2 x+1 x+2 Example f)

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