Determining Chord Length

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Presentation transcript:

Determining Chord Length Lesson 86

Theorem 86-1 If two chords intersect in a circle, then the products of the chord segments are equal. 𝐴𝐸 𝐸𝐵 = 𝐶𝐸 𝐸𝐷

In the circle, chords 𝐴𝐵 and 𝐶𝐷 intersect at point 𝑃. Find 𝑃𝐷. 𝐴𝑃 𝑃𝐵 = 𝐶𝑃 𝑃𝐷 4 9 = 6 𝑃𝐷 36=6 𝑃𝐷 𝑃𝐷=6

Find the value of 𝑧 in the diagram. Dimensions are in meters. 6.4𝑧=3.2 9.5 𝑧= 3.2 9.5 6.4 𝑧=4.75 𝑚

Find the value of 𝑚 in the diagram 2 𝑚+7 =4 8−𝑚 2𝑚+14=32−4𝑚 6𝑚+14=32 6𝑚=18 𝑚=3

Looking Forward Determining chord lengths prepares students for: Lesson 97: Concentric Circles Lesson 101: Determining Lengths of Segments Intersecting Circles Lesson 104: Relating Arc Lengths and Chords Lesson 106: Circumscribed and Inscribed Figures