# Tagged Questions

40 views

### Determine missing angle in polygon

I'm trying to figure out this question: Determine the measure of angle a I'm guessing $a=96\unicode{0186}$ using the following work: $$a = 180 - 84 = 96$$ ...
48 views

### Bisectors of adjacent angles of a parallelogram meet on midline?

Suppose $KLMN$ is a parallelogram, and that the bisectors of angle $K$ and angle $L$ meet at point $A$. Prove that $A$ is equidistant from $\overline{LM}$ and $\overline{KN}$, without using ...
43 views

### What kind of shape?

To construct this shape, draw a circle. Place the compass on a point on the circle and draw an arc of the same radius as the circle. Now place the compass at the intersection of the arc and the circle ...
78 views

### A convex $n$-gon and the $n$-gon made by its $n$ medians

For a convex $n$-gon $P_1P_2\cdots P_n$, let $M_i$ be the mid-point of the line segment $P_iP_{i+1}\ (i=1,2,\cdots,n)$ where $P_{n+1}=P_1$. Also, let $Q_1Q_2\cdots Q_n$ be an inner $n$-gon made by $n$ ...
27 views

### Where are $A,B,C$ in the regular $n$-gon such that $\min (|AB|+|BC|,|BC|+|CA|,|CA|+|AB|)$ gives the max?

Let $F_n$ be the regular $n$-gon of edge-length $1$. Let us consider taking three points $A, B, C$ in $F_n$. Suppose that you can take a point on the edge of $F_n$. Supposing that $|AB|$ represents ...
74 views

### Repeating an operation infinitely makes any convex $n$-gon a regular $n$-gon?

For any convex $n$-gon $P_{0,1}P_{0,2}\cdots P_{0,n}$, let us consider the following operation : Operation : Let $k=0,1,\cdots$. Take $n$ points $P_{k+1,i}\ (i=1,2,\cdots,n)$ outside of $n$-gon ...
142 views

### Prove using integration "circle is a polygon when number of sides-> infinity

Is there a proof of "if number of sidesof a regular polygon ->infinitythe regular polygon -> circle." using integration?
25 views

### About the relation between two regular icosahedrons and a regular dodecahedron

Let $C$ be the regular icosahedron, each of whose vertex exists at the centroid of the each surface of the regular dodecahedron $B$, each of whose vertex exists at the centroid of the each surface of ...
86 views

### About the diagonals whose length is an integer multiple of the edge length of a regular polygon

Are the followings true? 1. In every diagonal of every regular polygon, some diagonals of regular hexagon, whose lengths are twice as long as its edge length, are the only diagonals such that the ...
78 views

### About intersection points of some diagonals of a regular $n$-gon

Are my expectations true? My expectation 1 : There exist some intersection points, which are not on the center of the regular $n$-gon, of three or more diagonals when you draw all diagonals of a ...
180 views

### Internal polygon formed by drawing diagonals in a regular polygon

In an n-sided (n>4) regular polygon, label the vertices {0, 1, ..., n-1}. For each vertex i, draw a pair of diagonals: from i to (i+2) mod n and from i to (i-2) ...
58 views

### Finding every $(m,n)$ such that a regular $n$-gon is inscribed inside a regular $m$-gon.

I found the following five types. 1. $(m,n)=(kn,n)$ for $n\ge3, k\ge1$. 2. $(m,n)=(hk,2k)$ where $h\ge1$ is an odd number and $k\ge2$. 3. $(m,n)=(m,3)$ where $m\ge4$ and $m\not\equiv0$ (mod $3$). ...
44 views

### I do't understand how to do this problem and was wondering how to get the answer easily 180(n-2) n= the number of sides a figure has.

Please help with this poblem I nedd help with the basics of it. $180(n-2) n$= the number of sides a figure has.
84 views

### Are there any Heron-like formulas for convex polygons?

Are there any Heron-like formulas for convex polygons ? By Heron-like I mean formulas without angles as arguments and which takes as arguments only lenghts of sides of polygon - that is - we know no ...
333 views

### Relationship between the sides of inscribed polygons

In my math textbook there's a demonstration for the calculus of the circumference of a circle that involves regular polygons inscribed in the circle, but I don't get it. The book gives the following ...
I can imagine a quadrilateral where one of the angles is $180^\circ$. Is this still considered a quadrilateral? More generally, is every $n$-gon also a $(n+1)$-gon (for $n \ge 3$)?