SME
Grade 10 Math · Problem type
Two chords crossing
Use this for “Chords AB and CD cross at E; AE = 6, EB = 4 and CE = 3. Find ED.”
Diagram
Chords crossing inside a circle: the products of their parts are equal.
Products: AE × EB = CE × ED
6 × 4 = 3 × 8 = 24
This is an example. Type your own values to start a new problem.
AE
×
EB
=
CE
×
ED
Formulas
AE × EB = CE × ED
6 × 4 = 3 × 8
Assumptions
•
Two chords cross at E inside the circle.
•
The products of the parts of each chord are equal: AE × EB = CE × ED.
Step-by-step
WE KNOW
AE = 6, EB = 4, CE = 3
FIND
ED (ED)
Step 1 · Find ED (ED)
Use AE × EB = CE × ED
Crossing chords: the products of their parts are equal.
ED
=
AE
×
EB
CE
ED
=
6
×
4
3
ED
=
24
3
ED = 8
Check
Put the numbers back in. Both sides should match.
6 × 4 = 3 × 8 ✓
Topic check
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