MathematicsChapter 9: Chord and Arcs of a Circle
Longest Chord
A diameter has distance 0 from O and is longest.
Learning objectives
- Define and explain longest chord.
- Apply longest chord to a focused FBISE question.
- Check the answer for correct terms, evidence, working, and units.
Definition
A diameter has distance 0 from O and is longest. As the foot M moves toward the rim, the chord shrinks. Pythagoras: half-chord = sqrt(r^2 - d^2).
Formula
chord = sqrt(r2 - d2).
Where / symbols
- Longest Chord
- A diameter has distance 0 from O and is longest. As the foot M moves toward the rim, the chord shrinks. Pythagoras: half-chord = sqrt(r^2 - d^2).
Relationship
- equal chords <=> equal distance
Overview
Learn the idea, then use it:
Core Understanding
A diameter has distance 0 from O and is longest. As the foot M moves toward the rim, the chord shrinks. Pythagoras: half-chord = sqrt(r^2 - d^2).
Examples diameter longest · equal chords <=> equal distance · LONGEST CHORD: A diameter has distance 0 from O and is longest. As the foot M moves toward the rim, the chord shrinks. Pythagoras: half · Exam tip: Equal distance means the perpendicular distances, not the lengths along a radius to an endpoint (tho
Exam Application
State the correct term, connect it to the chapter rule or evidence, and use a clear example or calculation.
Examples Define first · Show the rule or evidence · Check units, labels, and conclusion
WHAT — LONGEST CHORD
A diameter has distance 0 from O and is longest. As the foot M moves toward the rim, the chord shrinks. Pythagoras: half-chord = sqrt(r^2 - d^2).
HOW — Use the idea
Identify what is given, select this topic's rule or evidence, apply it one step at a time, and check the result.
In simple words
Do not merge longest chord with a neighbouring idea that uses a different definition, rule, or method.
Key points
- diameter longest
- equal chords <=> equal distance
- LONGEST CHORD: A diameter has distance 0 from O and is longest. As the foot M moves toward the rim, the chord shrinks. Pythagoras: half
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Longest Chord
Sticky Notes · Quick Revision
Core Idea
- A diameter has distance 0 from O and is longest.
Key Points
- diameter longest
- equal chords <=> equal distance
- LONGEST CHORD: A diameter has distance 0 from O and is longest. As the foot M moves toward the rim, the chord shrinks. Pythagoras: half
Simple Check
- Explain longest chord in your own words and connect it to one chapter example.
How to Answer
- Define the idea, show the main rule or evidence, apply it, and check the final statement.
Common Mistake
- Do not merge longest chord with a neighbouring idea that uses a different definition, rule, or method.
FBISE Exam Tip
- Use the exact term, show working where needed, and include units or labelled evidence.
60-second revision
- A diameter has distance 0 from O and is longest.
- diameter longest
- equal chords <=> equal distance
- LONGEST CHORD: A diameter has distance 0 from O and is longest. As the foot M moves toward the rim, the chord shrinks. Pythagoras: half
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