1. Determining Chord Length
Lesson 86

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

3. 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

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

5. 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

6. 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