MathematicsChapter 10: Tangents and Angles of a Circle
The Picture
Inner circle radius r, outer R.
Learning objectives
- Define and explain the picture.
- Apply the picture to a focused FBISE question.
- Check the answer for correct terms, evidence, working, and units.
Definition
Inner circle radius r, outer R. Chord of the outer touches the inner at T. Then OT perp the chord and OT=r, so d=r for every such chord.
Mathematical form
OT=r
d=r for every such chord.
Where / symbols
- The Picture
- Inner circle radius r, outer R. Chord of the outer touches the inner at T. Then OT perp the chord and OT=r, so d=r for every such chord.
Relationship
- d = inner radius
Overview
Learn the idea, then use it:
Core Understanding
Inner circle radius r, outer R. Chord of the outer touches the inner at T. Then OT perp the chord and OT=r, so d=r for every such chord.
Examples d = inner radius · same centre · outer chord tangent to inner · THE PICTURE: Inner circle radius r, outer R. Chord of the outer touches the inner at T. Then OT perp the chord and OT=r, so d=r for e
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 — THE PICTURE
Inner circle radius r, outer R. Chord of the outer touches the inner at T. Then OT perp the chord and OT=r, so d=r for every such chord.
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 the picture with a neighbouring idea that uses a different definition, rule, or method.
Key points
- d = inner radius
- same centre
- outer chord tangent to inner
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.The Picture
Sticky Notes · Quick Revision
Core Idea
- Inner circle radius r, outer R.
Key Points
- d = inner radius
- same centre
- outer chord tangent to inner
Simple Check
- Explain the picture 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 the picture 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
- Inner circle radius r, outer R.
- d = inner radius
- same centre
- outer chord tangent to inner
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