1. **Problem Statement:** We have two chords intersecting inside a circle. One chord is divided into two segments of lengths 14 and 64. We want to find the length of the other chord's segments or verify the relationship between the segments. 2. **Relevant Formula:** When two chords intersect inside a circle, the products of the lengths of the segments of each chord are equal. This is called the Intersecting Chords Theorem: $$ AE \times EB = CE \times ED $$ where $AE$ and $EB$ are the segments of one chord, and $CE$ and $ED$ are the segments of the other chord. 3. **Given:** One chord has segments 14 and 64, so: $$ AE = 14, \quad EB = 64 $$ 4. **Calculate the product:** $$ AE \times EB = 14 \times 64 = 896 $$ 5. **Interpretation:** The product of the segments of the other chord must also be 896: $$ CE \times ED = 896 $$ 6. **Conclusion:** Without additional information about one segment of the other chord, we cannot find the exact lengths, but we know their product must be 896. This theorem helps solve problems involving intersecting chords in circles by relating segment lengths through multiplication.