What you’ll learn
Solve chord problems.
Key idea
A perpendicular from the center bisects the chord; the radius is the right-triangle hypotenuse.
A center perpendicular bisects the chord; use half-chord in the right triangle then restore both halves.
Worked example
Enter the exact value or ordered values in the format requested below.
Circle O has radius 39 cm. Its perpendicular to chord AB meets AB at M with OM=36 cm. Find the full chord AB in centimeters.
- The center perpendicular makes AM=MB.
- AM^2=39^2-36^2=225, so AM=15 and AB=2*15=30 cm.
Answer: 30
Quick Check
Evaluate a worked attempt at solve chord problems, identify the first invalid step, and provide the correction.
A circle has radius 29 and perpendicular center-to-chord distance 21. Step 1 computes half-chord=sqrt(29^2-21^2)=20. Step 2 reports the full chord as 20. Locate the first invalid step and correct it.