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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.

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*

This is a very good post..