---### Geometry Problem on Chords of a Circle7. In the accompanying diagram of circle \( O \), chords \( AB \) and \( CD \) intersect at \( E \). Given that \( AE = 5 \), \( CD = 18 \), and \( ED = 8 \), find the length of \( EB \).#### Diagram Explanation:- The circle has its center labeled \( O \).- Chord \( AB \) intersects chord \( CD \) at point \( E \) inside the circle.- Given measurements: - \( AE = 5 \) - \( CD = 18 \) - \( ED = 8 \)To find the length of \( EB \), apply the intersecting chords theorem (also known as the Power of a Point Theorem), which states: \[ AE \times EB = CE \times ED \]Based on the diagram, derive the unknown lengths.##### Provided Geometry Figure:- Circle with center \( O \)- Intersecting chords \( AB \) and \( CD \) with intersection point \( E \)- Labeled points \( A, B, C, D, \) and \( E \) --- **Question:**In the accompanying diagram of circle \( O \), chords \( \overline{AB} \) and \( \overline{CD} \) intersect at \( E \). If \( AE = 4 \), \( EB = 9 \), and \( CE = 6 \), what is the length of \( \overline{ED} \)?**Diagram description:**The diagram depicts a circle labeled \( O \) with two intersecting chords, \( \overline{AB} \) and \( \overline{CD} \). The point of intersection inside the circle is labeled \( E \). The segments are labeled as follows:- \( \overline{AE} = 4 \)- \( \overline{EB} = 9 \)- \( \overline{CE} = 6 \)The segment \( \overline{ED} \) is what needs to be found based on the given information.**Solution:**To solve the problem, we can make use of the property of intersecting chords in a circle which states that the product of the segments of one chord is equal to the product of the segments of the other chord.Using the given values:- \( AE \times EB = CE \times ED \)- Plugging in the values: \( 4 \times 9 = 6 \times ED \)- Simplifying: \( 36 = 6 \times ED \)- Solving for \( ED \): \( ED = \frac{36}{6} = 6 \)Therefore, the length of \( \overline{ED} \) is \( 6 \).

Name: ---### Geometry Problem on Chords of a Circle7. In the accompanying d
Uploaded: 2024-03-20T06:46:14.000Z
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Description: ---### Geometry Problem on Chords of a Circle7. In the accompanying diagram of circle \( O \), chords \( AB \) and \( CD \) intersect at \( E \). Given that \( AE = 5 \), \( CD = 18 \), and \( ED = 8 \), find the length of \( EB \).#### Diagram Expl