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To solve this problem, let's analyze the diagram and the given information.

The diagram shows two congruent line segments that intersect at the center of the circle. The segments are labeled as follows:
- One segment is divided into parts labeled \( x + 3 \) and \( 5 \).
- The other segment is divided into parts labeled \( 8 \) and an unspecified length.

Since these segments are congruent, the total lengths of each segment must be equal.

Let’s denote the unknown length on the second segment as \( y \). We have:
\[
x + 3 + 5 = 8 + y
\]
\[
x + 8 = 8 + y
\]
Since \( y \) must equal \( x \), we substitute and solve for \( x \). Since the segments are congruent, their total lengths should be the same.

The total length of the first segment is \( x + 3 + 5 \), which simplifies to \( x + 8 \). The other segment’s total length is \( 8 + x \). Therefore:
\[
x + 8 = 8 + x
\]
As it is already clear, we don’t need any adjustments, and the lengths of the parts should already match. We need to add up to get the total:

The total lengths are:
- Length of one segment: \( x + 3 + 5 \)
- Each congruent length: just doubled for total.

Therefore:
Congruent segment value from total leading to the following expected standard

The calculation with more answer match the intended expected sum helping in figuring overall cases here.

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Given two congruent segments that intersect each other. The end points of each segment are on a circle as shown in the figure below. The total length of the segments is ...

Learn how to solve a geometry problem involving two congruent segments intersecting in a circle. This problem covers the intersecting chords theorem and segment length congruence. Suitable for students in Grades 9-10.

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