Finding the center of a circle can be quite tricky in some cases, but has a practical and important applications. For instance, an ancient broken plate is unearthed and the archaeologist wants to find the length of its diameter, he can just find its center. Once the center is found, he can also find the […]

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# Posts tagged with 'inscribed angle theorem'

## A Proof that the Vertex Angle Sum of a Pentagram is 180 degrees

The pentagram is a five-pointed star. It was used by the ancient Greeks as a symbol of faith. In this post, we exhibit the mathematics of pentagrams — we show that the sum of the angle measures of its vertices equals 180°. For regular pentagrams, the proof is simple. By the inscribed angle theorem, the […]

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## The Proof of the Tangent Half-Angle Formula

In this post, we prove the following trigonometric identity: . Proof Consider a semi-circle with “center” and diameter and radius equal to 1 unit as shown below. If we let , then by the Inscribed Angle Theorem, . Draw perpendicular to as shown in the second figure. We can compute for the sine and cosine […]

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