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The image shows a geometric diagram with triangle relationships, specifically dealing with angles and side lengths. From the given information:

- \( A \), \( B \), \( C \), and \( D \) are points in the diagram.
- \( \triangle ABE \) and \( \triangle ACD \) are isosceles triangles, as the sides \( AB = AE \) and \( AD = AC \) are marked equal.
- \( E \) is the midpoint of \( AB \), and there is a right angle \( \angle EAC = 90^\circ \), suggesting that triangle \( AEC \) is a right triangle.
- \( CD = 8 \) units, and the goal is to find the length \( x \), which is the side \( BC \).

Given the relationships, we can apply the Pythagorean theorem and the properties of isosceles triangles to solve for \( x \). I'll begin by calculating \( x \).From the calculation, it seems that the value of \( x \) is 0, which does not align with the geometric context of the problem.

I will review the diagram further. It appears the relationship of the triangle may require additional geometric principles beyond just the Pythagorean theorem—such as applying the Law of Cosines or considering the isosceles triangle properties in conjunction with the given angles.

Let me revisit the problem with these additional considerations.

Find the value of x in the given geometric diagram with triangles ABE, ACD, and angles and side lengths marked.

Learn how to find the length of side x in a geometric diagram with triangles ABE and ACD using properties of isosceles triangles, Pythagorean theorem, and angles. This solution involves key geometry concepts such as isosceles triangles and right angles, suitable for students in Grades 9-12.

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