@mathematics.proofs 1 October 2020 edited more from that month

Circle Theorem Proof: Angle subtended at centre of circle is twice angle at circumference

In this article I'll be showing you how to prove that **the angle subtended at the centre of the circle is twice the angle at the circumference**. It is recommended that you ****watch the video below**** whilst reading to comprehend the proof fully. https://youtu.be/nq_VItzSj1M Firstly: **2x + A = 180** **2y + B = 180** This means that: **A = 180 - 2x** **B = 180 - 2y** Let's say that the angle beside 'A' is 'C', and that the angle next to 'B' is 'D'. Because half way around a circle is 180 degrees, we'd have to say that: **A + C = 180** **B + D = 180** This implies that **C = 180 - A** and that **D = 180 - B**. Since **A = 180 - 2x** and **B = 180 - 2y**: **C = 180 - (180 - 2x) = 180 - 180 + 2x = 2x** **D = 180 - (180 - 2y) = 180 - 180 + 2y = 2y** As **C = 2x** and **D = 2y**: **C + D = 2x + 2y = 2(x+y)** Now, since this is the case, ****it is true**** that **the angle subtended at the centre of the circle is twice the angle at the circumference**. *Article written by Tiago Hands:* *https://www.instagram.com/tiago_hands* *For more mathematics proofs, visit:* *https://www.instagram.com/mathematics.proofs* *To subscribe to maths content, go to:* *https://read.cash/@mathematics.proofs* *Lead image: By* *OpenClipart-Vectors* *from Pixabay* https://pixabay.com/users/openclipart-vectors-30363/?utm_source=link-attribution&utm_medium=referral&utm_campaign=image&utm_content=153262