1)if DE=6, EB=4, and AE=3, find EC D. B. E.

Elementary Geometry For College Students, 7e
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ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
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## Classwork #65

#### Name: ____________________

### Aracely Martinez Moreno

1. **If DE = 6, EB = 4, and AE = 3, find EC**

*Diagram*: The diagram depicts a circle with four points on its circumference labeled A, B, C, and D. The points are connected with chords, creating a quadrilateral inside the circle. Point E is the intersection of the chords AC and BD.

   - Points: A, B, C, and D lie on the circumference, while E is the intersection within the circle.
   - Given lengths: DE = 6, EB = 4, and AE = 3.

### **Explanatory Note for the Next Question:**
Continuing with a similar type of problem:

3. **If AB = 15, BE = 6, and CE = 12, find DE**

*Diagram*: Another circle with four points on the circumference labeled A, B, C, and D, in which chords intersect at point E inside the circle.

   - Points: A, B, C, and D lie on the circumference, while E is the intersection within the circle.
   - Given lengths: AB = 15, BE = 6, and CE = 12.

Use the intersecting chords theorem to solve for the unknown segment lengths in both cases. The theorem states that for two intersecting chords, 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.
Transcribed Image Text:## Classwork #65 #### Name: ____________________ ### Aracely Martinez Moreno 1. **If DE = 6, EB = 4, and AE = 3, find EC** *Diagram*: The diagram depicts a circle with four points on its circumference labeled A, B, C, and D. The points are connected with chords, creating a quadrilateral inside the circle. Point E is the intersection of the chords AC and BD. - Points: A, B, C, and D lie on the circumference, while E is the intersection within the circle. - Given lengths: DE = 6, EB = 4, and AE = 3. ### **Explanatory Note for the Next Question:** Continuing with a similar type of problem: 3. **If AB = 15, BE = 6, and CE = 12, find DE** *Diagram*: Another circle with four points on the circumference labeled A, B, C, and D, in which chords intersect at point E inside the circle. - Points: A, B, C, and D lie on the circumference, while E is the intersection within the circle. - Given lengths: AB = 15, BE = 6, and CE = 12. Use the intersecting chords theorem to solve for the unknown segment lengths in both cases. The theorem states that for two intersecting chords, 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.
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