When two chords intersect inside a circle, the products of their segments are equal — a key geometry concept tested on the DAT and OAT Quantitative Reasoning section.
Question:
In the diagram below, two chords AB and CD intersect at point O.
Answer:
Using the Intersecting Chords Theorem:
AO × OB = CO × OD
Let OD = x, then AO = x – 6
6(x – 6) = 5x
x = 36
AO = 36 – 6 = 30 ✅
Answer: A (30)
📘 For hundreds more practice problems like this one, check out the Math Destroyer — part of the DAT Destroyer Series by Dr. Jim Romano.
👉 2025 Math Destroyer | 720 DAT & OAT Quantitative Reasoning Questions
Question:
In the diagram below, two chords AB and CD intersect at point O.
- OB = 6
- AO is 6 units less than OD
- CO = 5
Find AO.
Answer:
Using the Intersecting Chords Theorem:
AO × OB = CO × OD
Let OD = x, then AO = x – 6
6(x – 6) = 5x
x = 36
AO = 36 – 6 = 30 ✅
Answer: A (30)
📘 For hundreds more practice problems like this one, check out the Math Destroyer — part of the DAT Destroyer Series by Dr. Jim Romano.
👉 2025 Math Destroyer | 720 DAT & OAT Quantitative Reasoning Questions
