https://file.aiquickdraw.com/mathbot/file/17263901094284qrzk84o.jpg

The problem is written in Indonesian and translates to:

"In the cyclic pentagon ABCDE, \(\angle ABD = 90^\circ\), \(BC = CD\), and \(AE\) is parallel to \(BC\). If \(AB = 8\) and \(BD = 6\), find the length of \(AE\)."

### Let's break it down:

1. **Cyclic Pentagon**: ABCDE is cyclic, meaning the points A, B, C, D, E lie on a common circle.
2. **\(\angle ABD = 90^\circ\)**: This implies triangle ABD is a right triangle.
3. **\(BC = CD\)**: The segments BC and CD are of equal length.
4. **\(AE \parallel BC\)**: AE is parallel to BC.
5. **Given values**:
   - \(AB = 8\)
   - \(BD = 6\)

### To solve:
We will apply the Pythagorean theorem in triangle ABD, as \(\angle ABD = 90^\circ\).

Using the theorem:
\[
AB^2 = AE^2 + BD^2
\]

Substituting the known values:
\[
8^2 = AE^2 + 6^2
\]
\[
64 = AE^2 + 36
\]
\[
AE^2 = 64 - 36 = 28
\]
\[
AE = \sqrt{28} = 2\sqrt{7}
\]

Thus, the length of \(AE\) is \(2\sqrt{7}\).

Would you like a more detailed explanation, or do you have any questions about this solution?

### 5 Related Questions:
1. How does the Pythagorean theorem apply to cyclic polygons?
2. What other properties can be derived from a cyclic pentagon?
3. How would the solution change if \(AB\) and \(BD\) were different?
4. What are the implications of having \(AE \parallel BC\) in this context?
5. How does the equality of \(BC\) and \(CD\) help in geometric constructions?

### Tip:
Always look for symmetry and parallelism in geometric problems, as they often simplify the solution process.

Pada siklik segi lima ABCDE, ABD = 90°, BC = CD, dan AE sejajar dengan BC. Jika AB = 8 dan BD = 6, tentukan AE.

Solve a cyclic pentagon geometry problem where angle ABD = 90°, AE is parallel to BC, and AB = 8, BD = 6. Learn how to apply the Pythagorean theorem to find the length of AE.

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