Talk:Cyclic quadrilateral

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I was wondering - does anyone have a proof for the first and/or fifth item(s) in the list? Aleph2.0 01:19, 22 May 2006 (UTC)

The first external link proves the first item on the list. Lemmy Kilmister 16:35, 13 June 2006 (UTC)

Question: If one the sides of cyclic quadrilateral is equal to radius, is the qudrilateral a square. Explain with proof please. —The preceding unsigned comment was added by 192.88.212.44 (talk • contribs).

Do concave or crossed quadrilaterals whose vertices lay on a circle count as cyclic quadrilaterals? For example, des Brahmagupta's formula apply to them to? Maybe it is worth mention wether or not this is the case in the article. 130.89.167.52 18:33, 19 October 2006 (UTC)

Improving the article
see if square insribed in circle whose radius isequal to side of square will not possible because it violates phythagoras thm. angle betn sides is 90 degree and two adjacent sides with diagonalis a diameter which is equal to 2r notsquare root *r$$Insert formula here$$ —Preceding unsigned comment added by Srinivas veldandi (talk • contribs)

Could someone redirect "circumscribed square" to cyclic quadrilateral?

It was not immediately clear to me that these are more or less the same thing. I'd think that the opportunity for confusion would be reduced if "circumscribed square" were redirected to "cyclic quadrilateral."


 * They are not the same thing. I think doing the redirection you suggest would cause more confusion, not less. —David Eppstein (talk) 06:46, 30 May 2009 (UTC)

Squared Circle?
The main article could be improved if there were reference to the drawing of a quadrilateral (specifically, a "square") around a circle so that each of its sides were touched. 216.99.219.12 (talk) 06:30, 30 May 2009 (UTC)


 * Maybe you're looking for tangential quadrilateral? Those are the ones that can be drawn with the quadrilateral outside and the circle inside. The ones here are the other way around. —David Eppstein (talk) 06:46, 30 May 2009 (UTC)

Missing minus sign?
The section "Area" currently says:


 * Provided A is not a right angle, the area can also be expressed as [Durell, p.26]
 * $$K = \tfrac{1}{4}(a^2-b^2-c^2+d^2)\tan{A}.$$

I think this needs to be multiplied by -1 to be correct. For example, as d goes to zero we have the case of a triangle, and the formula above gives


 * $$K = \tfrac{1}{4}(a^2-b^2-c^2)\tan{A}.$$

Now if A is acute, $$a^2-b^2-c^2$$ is negative while tan(A) is positive, while both of these are reversed if A is obtuse; in either case this gives a negative area. Multiplying it by -1 gives the correct triangle formula.

Could someone with access to the source check this out? Loraof (talk) 20:51, 9 January 2015 (UTC)


 * I withdraw the above post. The flaw is that letting d go to zero does not preserve the angle A. To preserve A, we have to let c go to zero; then the angle-side sequence becomes AaBbCd with b opposite A, and the formula is correct without multiplying by -1. Sorry about that! Loraof (talk) 14:52, 10 January 2015 (UTC)

Pascal Points
The article mentions Pascal points, but has no link to another Wikipedia page (there is no page on Pascal points), and no explanation of what a Pascal point is other than a reference to an article and a figure from which you can (at least) get an idea of what it is. If Pascal points are well known I feel I should at least have heard about them as a mathematician myself; or that I should have been able to find something via Google search or a search to Wolfram MathWorld, which I wasn't. What I'm getting at is: I think a short explanation of what a Pascal point is in order.

I realize the concept is not that easily explained in a short simple and concise way - otherwise I would have written it myself - but without the explanation I find this subsection useless as anything other than "Fun fact: There is this rule involving cyclic quadrilateral and some points".

Pascal Points may be related to Pascal's theorem (which I at least have heard of), but I could find no mention of them on that wiki-page either. —TheLoneGnu (talk) 08:59, 18 August 2020 (UTC)

Cyclic quadrilateral
Can we call a quadrilateral as cyclic if one of it's vertex is outside the circle but the sum of opposite angles is 180°? 2409:4064:703:26FD:0:0:283E:10A4 (talk) 05:36, 25 January 2022 (UTC)
 * Why do you think it is possible for both of those things to happen in a single quadrilateral? —David Eppstein (talk) 07:24, 25 January 2022 (UTC)

What is the need of it
What is the need of it 103.167.99.30 (talk) 05:39, 29 May 2022 (UTC)