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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).
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Longest Chord
What is it?
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).
In simple words
- 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
Important terms
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).
What you should learn
- Define and explain longest chord.
- Apply longest chord to a focused FBISE question.
- Check the answer for correct terms, evidence, working, and units.
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
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).
EXAM APPLICATION
State the correct term, connect it to the chapter rule or evidence, and use a clear example or calculation.
Recommended for Class 10
Full school-level explanation
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).
Learn the idea, then use it:
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.
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).
Remember
- 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
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.
Remember
- correct term
- chapter link
- clear application
Examples
- Define first
- Show the rule or evidence
- Check units, labels, and conclusion
Remember
- 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
- keep the ideas separate
- 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
- correct term
Deeper understanding
Go beyond memorising Longest Chord. Connect the definition to reasons, relationships, exceptions, and exam wording.
Common mistakes
Exam focus
Core Idea
Key Points
Simple Check
How to Answer
Exam focus
Quick revision
- 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
- keep the ideas separate
- Longest Chord: A diameter has distance 0 from O and is longest. As the foot M moves toward the rim, the chord shrin
- WHAT — LONGEST CHORD: A diameter has distance 0 from O and is longest. As the foot M moves toward the rim, the chord shrin
Do not merge longest chord with a neighbouring idea that uses a different definition, rule, or method.
For long answers on Longest Chord: define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important 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
- keep the ideas separate
Important formulas
- diameter longest
- equal chords <=> equal distance
- keep the ideas separate
Common exam traps
- Do not merge longest chord with a neighbouring idea that uses a different definition, rule, or method.
- Do not invent a formula, fact, unit, or diagram label that the chapter does not support.
Long question structure
Definition → key parts → example → exam caution
Common Mistakes
Common Mistakes
- Mistake
Do not merge longest chord with a neighbouring idea that uses a different definition, rule, or method.
- Mistake
Do not invent a formula, fact, unit, or diagram label that the chapter does not support.
- Mistake
Do not merge longest chord with a neighbouring idea that uses a different definition, rule, or method.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
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
keep the ideas separate
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).
equal chords <=> equal distance
- 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
- equal chords <=> equal distance
- Example
- diameter longest
- Critical warning
- Do not merge longest chord with a neighbouring idea that uses a different definition, rule, or method.
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Exam Practice
Define
Q1. Define Longest Chord.
Explain
Q2. Explain: CORE UNDERSTANDING.
Example
Q3. Give one clear example of Longest Chord and say why it fits.
Mistake
Q4. State one common mistake students make about Longest Chord.
Exam note
Q5. Write a short exam note on Longest Chord: definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.