Finding Segment Lengths When Chords Intersect
When two chords cross inside a circle, they create special relationships between the segments. The Segments of Chords Theorem states that if chords AB and CD intersect at point E, then EA × EB = EC × ED.
Think of this as a mathematical balancing act. The products of the segments on each chord must equal each other. This gives us a powerful equation to find missing segment lengths.
Let's see this in action! When solving these problems, we typically set up an equation using the theorem, substitute the given expressions, and solve for the variable. For example, if we know three segments measure x+1, x+2, and x+4, we can find the fourth segment by applying the theorem.
💡 Quick Tip: When chords intersect, always multiply the segments of each chord separately, then set these products equal. This pattern works no matter where the intersection point is located inside the circle.
