NCERT Solutions Class 9 Maths Chapter 9 Circles Exercise 9.1

Exercise 9.1 of Chapter 9 - Circles covers the basic concepts of circles, namely knowing the parts of a circle, the meaning of congruence of circles, and elementary theorems. NCERT Solutions Class 9 Maths Chapter 9 Circles Exercise 9.1 ideas help the students to develop solid reasoning and problem-solving skills that transcend geometry and higher classes.

1.0Download Class 9 Maths Chapter 9 Ex 9.1 NCERT Solutions PDF

You can download the complete and accurate NCERT Solutions Class 9 Maths Chapter 9 Circles Exercise 9.1  in PDF format for free. The NCERT Solutions are designed by qualified teachers, and are compliant with the CBSE curriculum which makes exam preparations easier, and more productive.

2.0Key Concepts of Exercise 9.1

• Learn about the definition of a circle and its key parts.
• The concept of congruent arcs and congruent circles.
• Key theorems based on circles.
• The application of geometric reasoning in problems and concepts about circles.

3.0CBSE Class 9 Chapter 9 Linear Equations Exercise 9.1 Comprises

1. Understanding Circles and its Parts.

• Learn about circles radius, diameter, chord, arc, sector, segment, and all the other components that constitute a circle. 
• Identifying visually the different parts and defining them through visuals.

2. Recognising Congruent Circles and Rectangles

• Exploring what it means for 2 circles to be congruent.
• Explore the concept of congruence in arcs of same, or equal circles.
• Use your knowledge in questions where geometry is practical.

3. Equal Chords and Their Properties

• Understand the simple theorem: Equal chords of a circle subtend equal angles at the center.
• Use logic and diagrams to identify equal chords.

4. Using Properties, Theorems and Diagrams

• Using the given diagram, prove circle-related theorems as key theorems, using a step-by-step logic approach.
• Note consistent angles, arcs and chords.
• Make proper use of notation and reasons in the write-up.

5. Logic and Proof Development

• Write basic geometric proofs involving equal chords to equal angles.
• Understand that logical steps are required when proving geometric ideas.
• Build a base that will help you increase your learning of the properties, e.g., tangents and cyclic quadrilaterals.

4.0NCERT Solutions Class 9 Maths Chapter 9: All Exercises

Here is a quick overview and access to solutions for all exercises from Chapter 9, Circles.

5.0Detailed CBSE Class 9 Chapter 9 Exercise 9.1 Solutions

• Recall that two circles are congruent if they have the same radii. Prove that equal chords of congruent circles subtend equal angles at their centres. Sol. Given : Two congruent circles $\mathrm{C}(0,\mathrm{r})$ and $\mathrm{C}\left({\mathrm{O}}^{\prime },\mathrm{r}\right)$ which have chords AB and CD respectively such that $\mathrm{AB}=\mathrm{CD}$.
  
  To prove : $\angle \mathrm{AOB}=\angle {\mathrm{CO}}^{\prime }\mathrm{D}$ Proof : From $△\mathrm{AOB}$ and $△{\mathrm{CO}}^{\prime }\mathrm{D}$, we have $\mathrm{AB}=\mathrm{CD}$ [Given] $\mathrm{OA}={\mathrm{O}}^{\prime }\mathrm{C}$ [Each equal to r] OB = O'D [Each equal to r] $\therefore △\mathrm{AOB}\cong △{\mathrm{CO}}^{\prime }\mathrm{D}$ [By SSS-congruence] $\Rightarrow \angle \mathrm{AOB}=\angle {\mathrm{CO}}^{\prime }\mathrm{D}[$ C.P.C.T. $]$
• Prove that if chords of congruent circles subtend equal angles at their centres, then the chords are equal. Sol. Given : Two congruent circle $\mathrm{C}(\mathrm{O},\mathrm{r})$ and $\mathrm{C}\left({\mathrm{O}}^{\prime },\mathrm{r}\right)$ which have chords AB and CD respectively, such that $\angle \mathrm{AOB}=\angle {\mathrm{CO}}^{\prime }\mathrm{D}$
  
  To prove : $AB=CD$ Proof : In $△\mathrm{AOB}$ and $△{\mathrm{CO}}^{\prime }\mathrm{D}$, we have :

6.0Key Features and Benefits: Class 9 Maths Chapter 9 Exercise 9.1

• Being Commands/Step-by-step NCERT Solutions that follow ...CBSE commands
• Concept is clearly conveyed with enough explain and diagrams
• Practice-based approach to allow for developmental reasoning based around theorems
• Base to learn on to gain a higher level examples in geometry with tangents and constructions
• Perfect for school/test/exams/olympiads!