In the circle shown, chords AC and BD intersect at E. AE=9, CE=4 and BD=15. Find the length of segments BE and ED.
Transcribed Image Text:**Intersecting Chords in a Circle**
This diagram illustrates two chords intersecting inside a circle.
- **Chord AB** and **Chord CD** intersect at point **E** within the circle.
Key points and measurements:
- **A**, **B**, **C**, and **D** are points on the circumference of the circle.
- **E** is the intersection point of chords **AB** and **CD**.
- The segment from point **A** to point **E** (AE) measures 9 units.
- The segment from point **E** to point **B** (EB) measures 4 units.
This demonstrates a fundamental geometric property: when two chords intersect inside a circle, the products of the lengths of the segments of each chord are equal. This property can be summarized as:
\[ AE \times EB = DE \times EC \]
Based on the given lengths:
\[ AE = 9 \quad \text{and} \quad EB = 4 \]
So:
\[ 9 \times 4 = DE \times EC \]
This property aids in solving many geometric problems involving circles and their chords.
Two-dimensional figure measured in terms of radius. It is formed by a set of points that are at a constant or fixed distance from a fixed point in the center of the plane. The parts of the circle are circumference, radius, diameter, chord, tangent, secant, arc of a circle, and segment in a circle.
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![**Intersecting Chords in a Circle**
This diagram illustrates two chords intersecting inside a circle.
- **Chord AB** and **Chord CD** intersect at point **E** within the circle.
Key points and measurements:
- **A**, **B**, **C**, and **D** are points on the circumference of the circle.
- **E** is the intersection point of chords **AB** and **CD**.
- The segment from point **A** to point **E** (AE) measures 9 units.
- The segment from point **E** to point **B** (EB) measures 4 units.
This demonstrates a fundamental geometric property: when two chords intersect inside a circle, the products of the lengths of the segments of each chord are equal. This property can be summarized as:
\[ AE \times EB = DE \times EC \]
Based on the given lengths:
\[ AE = 9 \quad \text{and} \quad EB = 4 \]
So:
\[ 9 \times 4 = DE \times EC \]
This property aids in solving many geometric problems involving circles and their chords.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F33ef17cf-3057-4313-84bc-763127c3429d%2F68529f8e-c5bf-44f7-8e43-1ac60f3fe193%2Fxnw222s_processed.png&w=3840&q=75)
