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

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

Segment Lengths in Circles
10.5 Segment Lengths in Circles

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!

D A C B E 9 3 x 6

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

C 8 A x E 2x 9 B D

C 15 A 10 E x+1 x D B

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

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

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

E A B C D 11 9 x 10

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

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

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

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

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