Geometry of Circles and Construction of Incircle and Centroid. Mathematics State Board, Class 9: lessons, tests, tasks.

1.	Introduction to circle
2.	Circle through three points
3.	Theorems on perpendicular from the centre to a chord
4.	Theorems on angle subtended by the chord at the centre
5.	Theorems on equal chords
6.	Theorems on angle at the centre and the circumference
7.	Special cases of angle at the centre and the circumference
8.	Theorems on angles at the circumference to the same segment
9.	Theorem on interior angles of a cyclic quadrilaterals
10.	Theorem on exterior angles of a cyclic quadrilaterals
11.	Construction of incircle of a triangle
12.	Construction of centroid of a triangle

1.	Multiple choice question I Difficulty: easy	2
2.	Multiple choice question II Difficulty: easy	2
3.	Multiple choice question III Difficulty: easy	2
4.	Multiple choice question IV Difficulty: easy	2
5.	Multiple choice question V Difficulty: easy	2
6.	Two marks example problems I Difficulty: medium	2
7.	Two marks example problems II Difficulty: medium	4
8.	Two marks example problems III Difficulty: medium	4
9.	Two marks example problems IV Difficulty: medium	4
10.	Two marks example problems V Difficulty: medium	5
11.	Two marks exercise problems I Difficulty: medium	4
12.	Two marks exercise problems II Difficulty: medium	4
13.	Two marks exercise problems III Difficulty: medium	2
14.	Five marks example problems I Difficulty: hard	0
15.	Five marks example problems II Difficulty: hard	5
16.	Five marks example problems III Difficulty: hard	0
17.	Five marks example problems IV Difficulty: hard	0
18.	Five marks example problems V Difficulty: hard	0
19.	Five marks exercise problems I Difficulty: hard	10
20.	Five marks exercise problems II Difficulty: hard	5
21.	Five marks exercise problems III Difficulty: hard	5
22.	Five marks exercise problems IV Difficulty: hard	5
23.	Five marks exercise problems V Difficulty: hard	5
24.	Five marks exercise problems VI Difficulty: hard	5
25.	Five marks exercise problems VII Difficulty: hard	5
26.	Five marks exercise problems VIII Difficulty: hard	5
27.	Five marks exercise problems IX Difficulty: hard	0
28.	Five marks exercise problems X Difficulty: hard	0
29.	Five marks exercise problems XI Difficulty: hard	0
30.	Five marks exercise problems XII Difficulty: hard	0
31.	Five marks exercise problems XIII Difficulty: hard	0
32.	Five marks exercise problems IX Difficulty: hard	0
33.	Five marks exercise problems X Difficulty: hard	0

1.	Choose the correct answer Difficulty: easy	2
2.	Knowing the parts Difficulty: easy	3
3.	Find the unknown angle Difficulty: easy	1
4.	Find the required angle Difficulty: medium	3
5.	Find the degree measure of 'x' Difficulty: medium	2
6.	Find the distance Difficulty: medium	4
7.	Find the area of the shaded region Difficulty: medium	2
8.	Find the angles from the figure Difficulty: medium	3
9.	Find the unknown angle 'y' Difficulty: medium	2
10.	Find the subtended angle Difficulty: medium	2
11.	Identify the theorem and analyse Difficulty: hard	4
12.	Find the chord length Difficulty: hard	4
13.	Prove the problem Difficulty: hard	4
14.	Explore the unknown angles Difficulty: hard	5

1.	Calculate the required angles of the cyclic quadrilateral Difficulty: hard	5
2.	Find the angle OAC Difficulty: hard	5
3.	Find the angle RPO Difficulty: hard	5

1.	Training test I Difficulty: medium	16
2.	Training test II Difficulty: medium	16
3.	Training test IV Difficulty: medium	21
4.	Training test V Difficulty: medium	8
5.	Training test VII Difficulty: medium	11

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Methodical recommendation

Geometry of Circles and Construction of Incircle and Centroid

Theory

Textbook Questions

Practice Questions

Key Questions for School Exam Preparation

Tests

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