Talk:Inscribed angle

Shouldn't this be included here?

Shouldn't the property of angles in the same arc being of the same size be discussed on this page as it is on the French article; or does it have its own page? — Preceding unsigned comment added by Swedish fusilier (talk • contribs) 09:56, 12 November 2007 (UTC)

I would agree and suggest someone translate the French article to replace this one, as the French article looks more comprehensive.--Waxsin (talk) 20:30, 7 May 2009 (UTC)

The figure in the article is somewhat misleading since the sides of inscribed angle pass through the center of the circle. A number of points need to be included to clarify the concept of an inscribed angle. The inscribed angle and central angle are opposite to each other and on different sides of a common chord. The lack of the common chord tends to disorient the first-time viewer. Inscribed angles on opposite sides of a chord usually have different values but their sum equals 180°. One could also note that two inscribe angles on the same side of the chord have the same values. --Jbergquist (talk) 09:10, 28 February 2011 (UTC)

The facts about inscribed angles mentioned above are the topic of Book 4, Propositions 20-22 of Euclid's Elements. --Jbergquist (talk) 23:10, 4 March 2011 (UTC)

Merger discussion

The following discussion is closed. Please do not modify it. Subsequent comments should be made in a new section. A summary of the conclusions reached follows.

Consensus for new subsection. -- P 1 9 9 • TALK 16:56, 21 March 2011 (UTC)

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• I feel that the article inscribed angle theorem should not be merged into this one, since it is more specific. The theorem could be a subsection of this article. Willow (talk) 18:50, 23 September 2008 (UTC)
• I feel both articles are poorly written in not being general enough. For instance it wasn't until I read the Circle#Inscribed_angles article that it was clearly mentioned that angles intercepting the same arc are equal, yet this is never explicitly proved in either article. Please explain how the inscribed angle theorem article is more "specific" as I can hardly tell the two articles apart--Waxsin (talk) 20:45, 7 May 2009 (UTC)
• I agree with Willow that both articles should not be merged. The inscribed angle theorem is simpler, better to understand. The other article gives a step by step proof but with symbols that most people can't even pronounce. --Bleuprint (talk) 21:14, 14 May 2009 (UTC)
• No merging. The inscribed angle theorem article should be summarized and copied as a sub-section. 70.171.224.249 (talk) 01:58, 28 April 2010 (UTC)

The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.

Why two proofs?

There are two subsections titled "proof", which on first glance seem to prove a similar theorem. Can somebody please explain the difference between these theorems? --Erel Segal (talk) 10:30, 4 February 2014 (UTC)

I'll fix it. 208.50.124.65 (talk) 21:22, 31 July 2014 (UTC)

External links modified

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Mention of the circumcircle (and the Circumcircle page)

I'm not suggesting a merger here at all, but shouldn't there be some discussion of how inscribed angles/triangles relate to the idea of a circumcircle as well as a link going to Circumcircle (other than the one in Template:Ancient_Greek_mathematics)? RW Dutton (talk) 05:31, 20 December 2024 (UTC)

Central Angle Theorem vs Inscribed Angle Theorem

This article seems to combine these two theorems and call it the "Inscribed Angle Theorem" or consider the "Incribed Angle Theorem" and the "Central Angle Theorem" as the same theorem.

However, in Euclid's Elements Book 3 Proposition 20, he first postulates and proves that an arc on a circle subtends a central angle that is twice that of an angle subtended by the same arc to a point on the circumference of the circle (specifically, the major arc). So this proposition consists of one central and one and only one inscribed angle.

In Book 3 Proposition 21, he then postulates and proves that the angles subtended by the same arc on a circle to points on the circumference of the circle (specifically the major arc) are of the same measaure. He uses the previous postulate (above) to support his proof. This proposition consists of two or more inscribed angles.

I submit that Book 3 Proposition 20 is the "Central Angle Theorem" and Book 3 Proposition 21 is the "Inscribed Angle Theorem" and are different, all be it related, theorems.

JeffCampsall (talk) 15:18, 21 August 2026 (UTC)

Whether you consider this to be one theorem or two is more or less a matter of personal preference. In Euclid per se, Proposition 21 is a trivial corollary of proposition 20, but if you want you can easily combine them, e.g. this example from a geometry textbook: "Inscribed angle theorem: Any inscribed angle of a circle equals half the bend of its intercepted arc". In literature I can find in searching the two names "central angle theorem" and "inscribed angle theorem" seem to be used somewhat interchangeably, and different sources pick one or the other to refer to the same result, or, if you like, to refer to either of these two results depending on what is needed for the problem assuming that readers can figure out what is intended. (The name "inscribed angle theorem" seems to be more common by a factor of 4–5x.) Extremely few sources I can find use both names to refer to two different things. –jacobolus (t) 17:11, 21 August 2026 (UTC)

I mostly reverted your change. I don't think we should belabor this discussion in the lead section. If you want to mention it, maybe we can figure out some way to do it unobtrusively. But I think you bring up a fair point, and I don't mean to reject your contribution entirely. I'm happy to work together to try to satisfy any issues you have with the way the article presents this.

If you want we could definitely directly quote Euclid's Elements from this article, and also could include more material about later mathematicians' commentaries on that section of the Elements. I'm not really an expert in the history of this theorem per se, but I'm sure plenty has been written about it if anyone wants to hit the library. –jacobolus (t) 01:10, 22 August 2026 (UTC)