Test Questions on Segment Lengths of Intersecting Chords

📚 Quick Study Guide

• 📐 Intersecting Chords Theorem: If two chords intersect inside a circle, then the product of the segments of one chord is equal to the product of the segments of the other chord.
• ✍️ Formula: If chords $AC$ and $BD$ intersect at point $E$ inside the circle, then $AE \cdot EC = BE \cdot ED$.
• 💡 Key Idea: Visualize the segments clearly. Draw diagrams to help identify each segment length.
• ➕ Algebra: Use algebraic equations to represent the segment lengths and solve for unknowns.
• 🧐 Example: If $AE = 4$, $EC = 6$, and $BE = 3$, then $ED = \frac{AE \cdot EC}{BE} = \frac{4 \cdot 6}{3} = 8$.

Practice Quiz

1. What is the length of segment $AE$ if $EC = 9$, $BE = 6$, and $ED = 3$?
1. 3
2. 4.5
3. 2
4. 18
2. If chords $AC$ and $BD$ intersect at $E$. $AE = 5$, $EC = 4$, and $BE = 2$, what is the length of $ED$?
1. 10
2. 8
3. 6
4. 2.5
3. Chords $RS$ and $TV$ intersect at point $U$ inside a circle. If $RU = 8$, $US = 6$, and $TU = 4$, find the length of $UV$.
1. 12
2. 10
3. 14
4. 16
4. Two chords, $PQ$ and $MN$, intersect at point $O$ inside a circle. If $PO = x$, $OQ = 6$, $MO = 3$, and $ON = 8$, find the value of $x$.
1. 4
2. 16
3. 24
4. 12
5. Chords $AB$ and $CD$ intersect at $E$. If $AE = 2x$, $EB = 3$, $CE = 4$, and $ED = 6$, find the value of $x$.
1. 2
2. 4
3. 6
4. 8
6. If $AE = x + 2$, $EC = x$, $BE = 4$, and $ED = 3$, what is the value of $x$?
1. 6
2. 4
3. 10
4. 2
7. Chords $FG$ and $HJ$ intersect at $K$. If $FK = 5$, $KG = x$, $HK = 2$, and $KJ = 10$, find the value of $x$.
1. 2
2. 4
3. 6
4. 8