Circles Theorem 9.5 | Class 9 2026 - 27 Prep | Proof and Logic | NCERT | Morning Star Academy скачать в хорошем качестве

Circles Theorem 9.5 | Class 9 2026 - 27 Prep | Proof and Logic | NCERT | Morning Star Academy

Class 9 Maths Chapter 9, Circles Class 9 Class 9 Maths 2026-27 | Theorem 9.5 Circles | Start Your Prep Early! In this video, we provide a detailed, step-by-step handwritten proof of Theorem 9.5 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 9.5. How to prove Class 9 Circles Theorem 9.5 Logical explanation of Congruent Triangles within Circles. Tips for presenting geometry proofs in your school exams. Mathematical Breakdown: Given: A circle with centre O and two equal chords AB and PQ (i.e., AB=PQ). Construction: Draw perpendiculars from the centre to the chords: OM⊥AB and ON⊥PQ. Join the centre to one end of each chord: Join OA and OP (these are the radii). To Prove: The chords are at equal distance from the centre, meaning OM=ON. Methodology: We utilize the SSS (Side-Side-Side) Congruence Rule to prove that △AOM≅△BOM. Mathematical Proof Step A: Use the Perpendicular Bisector Property We know that a perpendicular drawn from the centre of a circle to a chord bisects the chord. Since OX⊥AB, then AX=21​AB. Since OY⊥CD, then CY=21​CD. Since we are given that AB=CD, their halves must also be equal: 1/2 ​AB = 1/2 PQ ⟹AM=PN…(Equation 1) Step B: Prove Congruence of Triangles Now, consider the two right-angled triangles formed: △AMO and △PNO. Right Angle: ∠AMO=∠PNO (both 90∘ by construction). Hypotenuse: AO = PO (radii of the same circle). Side: AM = PN (proved in Equation 1). By the RHS (Right angle-Hypotenuse-Side) congruence criterion: △AMO≅△PNO Step C: Conclusion (CPCT) Since the triangles are congruent, their corresponding parts are equal: OM=ON (by CPCT) Theorem 9.4:    • Circles Theorem 9.4 | Class 9 2026 - 27  P...   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. Subscribe to join the Academy! 🌟 #Class9Maths #Circles #Theorem9.5 #NCERT #MorningStarAcademy #GeometryProof #circlestheorem9.5 #congruenceoftriangles #congruent #circlesclass9 #ncertsolutions #theorem9.5 #cbseclass9mathematics Link to the NCERT Textbook: https://amzn.to/3OtPLGj As an Amazon Associate, Morning Star Academy earns from qualifying purchases. This helps support our mission to provide free education to students. 0:00 Start 0:08 Recap 00:43 Th. 9.5, What does it say? 02:24 Construction - Why use dotted lines? 05:04 Given Identified, Construction mentioned 05:37 To prove - Th. 9.5 06:03 Proof of Th. 9.5 11:26 Th. 9.5 revision for exam class 9 maths theorem 9.5 theorem 9.5 class 9 maths circles theorem 9.5 class 9 ch 9 theorem 9.5 class 9 circles introduction theorem circlestheorem9.5, circles class 9, circles class 9 theorem 9.5, circles class 9 theorems, class 9 maths chapter 9, class 9th chapter circles theorem 9.5, circles theorem 5 class 9 circles rapid revision, class 9 circles theorems class 9 maths Class 9 Circles #theorem9.5class9 #circlestheorem9.5