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

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**Segment Lengths in Circles**

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. EA EB = EC ED D A C B E *We can set up a
proportion to find the
missing length!

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D A C B E 9 3 x 6

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Example a) D A C B E 12 8 6 x

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C 8 A x E 2x 9 B D

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C 15 A 10 E x+1 x D B

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Example e) x+1 C x+2 E x+3 A x+5 D B

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**external secant segment**

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. external secant segment tangent segment secant segment touches 2 places touches 1 place

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

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

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Example b) A 72 B 2 E 40 D C 78

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

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Secants, Tangents, and Angle Measures and Special Segments in a Circle

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