The angle subtended by a diameter at any point on the circle is 90° | Angle in semicircle is 90 |

Angle in a Semicircle is 90° | Proof of Angle Subtended by Diameter | Geometry Theorem In this video, we will learn the *proof of the theorem “Angle in a Semicircle is 90°”* in a simple and easy-to-understand way. This important theorem of circle geometry states that **the angle subtended by the diameter of a circle at any point on the circumference is always 90°**. If you are studying mathematics and want to understand the concept along with its mathematical proof, this video is for you! The theorem can also be stated as: *The angle subtended by the diameter at a point on the circle is a right angle.* In this video, we will explain why this angle is always equal to 90 degrees using the properties of circles and angles. Whether you are a Class 9 or Class 10 student, preparing for school examinations, revising geometry concepts, or strengthening your understanding of circle theorems, this explanation will help you understand the result and remember its proof. What You Will Learn in This Video In this video, you will learn: The statement of the theorem **Angle in a Semicircle is 90°**. What it means for a diameter to subtend an angle at a point on the circumference. How to identify the diameter, centre, and angle in a circle diagram. The step-by-step mathematical proof of the theorem. Why the angle formed at the circumference is always a right angle. How to use this theorem to solve geometry questions involving circles and triangles. How this important result can help you in school mathematics examinations. Statement of the Theorem *The angle subtended by the diameter of a circle at any point on the remaining circumference is 90°.* In other words, if AB is the diameter of a circle and P is any point on the circumference other than A and B, then: ∠APB = 90° Therefore, triangle APB is a right-angled triangle, with the right angle at P. Proof of Angle in a Semicircle We will prove the theorem using the properties of angles in a circle. By considering the centre of the circle and the angles subtended by the relevant chords, we can establish the relationship between the angles and show that the angle formed at the circumference is exactly 90°. Watch the complete video to understand each step of the proof, follow the geometrical reasoning, and learn how to present the result correctly in your examination. Why Is This Theorem Important? The angle in a semicircle theorem is one of the fundamental results in circle geometry. It is useful for identifying right-angled triangles, finding unknown angles, proving geometrical statements, and solving questions based on circles and triangles. Students should understand the proof instead of simply memorising the result. A clear understanding of this theorem makes it easier to solve more advanced geometry problems and apply other circle theorems correctly. This topic is particularly useful for students studying **NCERT Mathematics, Class 9 Mathematics, Class 10 Mathematics, circle geometry, and important geometry theorems**. Who Should Watch This Video? This video is useful for: Class 9 Mathematics students. Class 10 Mathematics students. Students learning circle theorems and geometry proofs. Students preparing for school tests and board examinations. Learners who want to revise important mathematical results. If you find this explanation helpful, like the video, share it with your classmates, and subscribe to *Pie Factor* for more mathematics lessons, theorem proofs, NCERT solutions, and step-by-step explanations. Keep learning mathematics with clear concepts and logical proofs! Timestamps: 00:00 Introduction to Angle in a Semicircle 00:35 Statement of the Theorem 01:20 Understanding the Circle Diagram 02:10 Important Properties of Circle Angles 03:00 Starting the Mathematical Proof 04:10 Step-by-Step Proof of the Theorem 05:40 Proving the Angle is 90° 06:50 Final Result and Conclusion 07:35 Quick Revision of the Theorem 08:15 Summary and Outro