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I am looking for a proof that: if $A_{11}A_{12}...A_{1n}$; $A_{21}A_{22}...A_{2n}$; $\cdots$; $A_{i1}A_{i2}...A_{in}$; $\cdots$; $A_{m1}A_{m2}...A_{mn}$ are $m$ oriented regular polygons ($n$-gons), w …

Please don't close this question. Because there is simple configuration with 57 vote up, and don't close. Why you vote up that question and You vote to close this question? A problem I posed at here …

When I read the new paper 100 CHARACTERIZATIONS OF TANGENTIAL QUADRILATERALS-section 7, I remember that I posed some problem associated with tangential quadrilateral from 2014 in here and 2015 in here …

The result as follows from special configuration of merge Nine Circle Theorem and Eight Circle theorem but it is new: Problem: Let three circle $(A)$, $(B)$, $(C)$ , let $A_c$ be arbitrary point in th …

I am looking for a proof of a generalization Napoleon theorem, Bottema theorem and Brahmagupta theorem and van Aubel theorem, and Finsler–Hadwiger theorem in one configuration, as follows: Let four po …

The solution of problem in our paper On an Extension of Miquel's Theorem to a Cyclic Hexagon; Relative configuration in here On the eight circles theorem and its dual

I am looking for a proof of the problem as follows: Let $ABC$ be a triangle, let points $D$, $E$ be chosen on $BC$, points $F$, $G$ be chosen on $CA$, points $H$, $I$ be chosen on $AB$, such that $IF$ …

An equilateral triangle constructed from a reference triangle is a topic which is intersested by plane geometry lovers. See Napoleon equilateral triangle, Morley equilateral triangle....In this topic …

This configuration appear as problem 3845 in Crux Mathematicorum. I see it is very beautiful. This configuration are generalization of Pascal theorem and Brianchon theorem: Consider six points $A_1$, …

I am looking for a proof or a reference request for a problem as follows: Problem: Let a cyclic hexagon with sidelines $l_1$, $l_2$, $l_3$, $l_4$, $l_5$, $l_6$ and $l_1 \cap l_4 =A$, $l_3 \cap l_6 = …

Abstract: In the figure belows: Three lines through center of pair opposite red circle are concurrent. This is a statement of Dao's theorem on six circumcenter, a new theorem in plane geometry which w …

I proposed a generalization of the Archimedean circle : In this figure $M$ is the midpoint of $AB$, $DE$; $(G)$, $(H)$, $(M)$ are the semicircles. Then two yellow circles are congruent. Question: Is t …

In this configuration as follows, we have a nice formula: $$\cos(\varphi)=\frac{OF.OE+OB.OC}{OF.OB+OE.OC}$$ Is the formula known? and can we generalized for higher dimensions?

Conjecture: Let $A_1, A_2,\dotsc,A_n$; $B_1, B_2,\dotsc,B_n$ and $C_1, C_2,\dotsc,C_n$ be $3n$ points in the plane such that $\angle{\overrightarrow{A_iB_i}, \overrightarrow{A_{i+1}B_{i+1}}}=\frac{2 …

Theorem 9.1 in this paper as follows is a generalization of Turker circle. Turker circles is a generalization of many circles as: Cosine Circle, circum circle, First Lemoine Circle, Gallatly Circle, K …