Class 9 Maths
- Topic Tree
- Terms and Definitions
- Activity – word search, cross word, mcq
- Important Theorems
- Minor arc and major arc problems
- Two circles intersecting at a common chord
- Circle Theorems – Sketch notes
- Find the length of a chord – problem
- Summary of circle theorems
- Centum Cyclic Unit Test Question Paper
- Key for CCUT
Topic Tree
1. Introduction
– Definition and examples of circles in real life.
2. Circles and Related Terms
– Circle, radius, diameter.
– Chords, arcs (major and minor), segments (major and minor), sectors (major and minor).
– Definitions and properties.
3. Angle Subtended by a Chord
– Angles subtended at the center and at a point on the circle.
– Relationship between the size of the chord and angle subtended.
4. Theorems
– Equal chords subtend equal angles at the center.
– Chords subtending equal angles are equal.
5. Perpendicular from the Center to a Chord
– Perpendicular bisector theorem.
– Converse: Bisected chords are perpendicular.
6. Circle Through Three Points
– Unique circle through three non-collinear points.
– Construction of circumcircle for a triangle.
7. Equal Chords and Their Distances
– Relationship between chord length and distance from the center.
– Equal chords are equidistant from the center.
– Converse: Equidistant chords are equal.
8. Angle Subtended by an Arc
– Congruent arcs subtend equal angles.
– Angle subtended by an arc at the center is double that at any point on the circle.
– Angles in the same segment are equal.
– Angle in a semicircle is a right angle.
9. Cyclic Quadrilaterals
– Definition and properties.
– Opposite angles sum to 180°.
– Converse theorem.
10. Optional Advanced Theorems (Exercises 10.6)
– Relationships involving intersecting chords and line of centers.
– Advanced circle properties in special cases like rhombuses and parallelograms.
11. Summary
– Consolidation of all key theorems and properties.
Terms and Definitions
ACTIVITY
Theorems
Equal chords
How to present a theorem in circles
