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Bellwork 1) (x+3)(x+7) 2) (2x+4)(x-4). 10.5 Segment Lengths in Circles.

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Presentation on theme: "Bellwork 1) (x+3)(x+7) 2) (2x+4)(x-4). 10.5 Segment Lengths in Circles."— Presentation transcript:

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

2 10.5 Segment Lengths in Circles

3 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!

4 D A C B E x

5 D A C B E Example a) x

6 D A C B E 8 9 2x x

7 D A C B E x+1 x

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

9 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.

10 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

11 E A B C D 11 9 x 10

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

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

14 E A B C D Example b)

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


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