Circles Theorem 9.4 | Class 9 2026 - 27 Prep | Proof and Logic | NCERT | Morning Star Academy

Описание: Class 9 Maths Chapter 9, Circles Class 9

Class 9 Maths 2026-27 | Theorem 9.4 Circles | Start Your Prep Early!

In this video, we provide a detailed, step-by-step handwritten proof of Theorem 9.4 from the Class 9 Maths NCERT chapter on Circles. We explain the logic behind "Equal chords of a circle subtend equal angles at the centre"

What You Will Learn:
Complete handwritten proof of Theorem 9.4.
How to prove Class 9 Circles Theorem 9.4
Logical explanation of Congruent Triangles within Circles.
Tips for presenting geometry proofs in your school exams.

Mathematical Breakdown:
Given: A circle with center O and a chord AB. M is the midpoint of AB such that AM=BM.
To Prove: OM⊥AB (meaning ∠OMA=∠OMB=90∘).
Methodology: We utilize the SSS (Side-Side-Side) Congruence Rule to prove that △AOM≅△BOM.
Key Concept: Since the radii are equal (OA=OB) and the midpoint is given (AM=BM), the triangles are congruent by SSS.
By CPCT, the angles ∠OMA and ∠OMB are equal; since they form a linear pair on the chord AB, each must be 90∘, proving the line is perpendicular.

Theorem 9.3:    • Circles Theorem 9.3 | Class 9 | Proof and ...  
Theorem 9.2:    • Circles Theorem 9.2 | Class 9 | Proof and ...  
Theorem 9.1:    • Circles Theorem 9.1 | Class 9 | Proof and ...  
Exercise 9.1:    • Circles Ex 9.1 | Class 9 | NCERT Solutions...  

Textbooks Covered: While we follow the NCERT curriculum, these concepts are essential for students using:
R.D. Sharma
R.S. Aggarwal
S. Chand & Pearson Foundation

About Morning Star Academy: We are building a comprehensive digital library of mathematics solutions. Our mission is to provide high-quality, step-by-step guidance for students aiming for academic excellence and competitive success.

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Link to the NCERT Textbook: https://amzn.to/3OtPLGj
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0:00 Start
0:50 Recap
01:03 Th. 9.4, what does it say?
01:34 Construction - Why use dotted lines?
03:25 Given Identified
04:00 To prove - Th. 9.4
04:26 Proof of Th. 9.4
06:43 Why ∠OMA is 90. Linear Pairs
08:14 Th. 9.4 revision for exam

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