# Questions tagged [geometric-construction]

Questions on constructing geometrical figures using a limited set of tools. The compass and straightedge are almost always allowed, while other tools like angle trisectors and marked rulers (neusis) may be allowed depending on context.

624 questions
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### Construction of a regular pentagon

In Robert Dixon's Mathographics, a regular pentagon is constructed with straightedge and compass only. It is the pentagon $ABCDE$ pictured below. I am having trouble seeing why the central angles ...
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### Can a regular heptagon be constructed using a compass, straightedge, and angle trisector?

Euclid has a magical compass with which he can trisect any angle. Together with a regular compass and a straightedge, can he construct a regular heptagon?
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### circle that touch quadrantal internally

I want to know how to construct circle that touch quadrantal(1/4 part of circle) internally. I spend several hours for solving this problem but I have no luck. I attached the picture what I've ...
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### Find the maximum area possible of equilateral triangle that inside the given square

How can I find the maximum area possible of equilateral triangle that inside a square whose sides have length a. And how does that triangle look like? Can we construct it (with compass and ...
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### How to determine the center of a circle with pen and straightedge [duplicate]

Possible Duplicate: Determine the centre of a circle My buddy draws a circle then he erase its center. He quiz me how can find the center with only pen and straightedge (no compass). Do you ...
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### The angle trisection problem

You have an angle and you have a pen, paper, compass and a straight edge. You don't know how big the angle is, divide this angle into three equal part using only the material that is listed here? If ...
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### Can a circle's circumference be divided into arbitrary number of equal parts using straight edge and compass only?

Can a circle's circumference be divided into arbitrary number of equal parts using straight edge and compass only? In other words, are all the $\frac{2\pi}{k} , k \in \mathbb N^+$ angles constructible?...
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### Determine the centre of a circle

Given a circle $O$ on a paper, we do not know the centre point. Can we draw the centre only using a ruler (by which we can only draw straight lines)? One fact I know: we can draw the tangent line at ...
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### Triangle from lengths of angle bisectors

According to http://www.cut-the-knot.org/triangle/TriangleFromBisectors.shtml it is impossible to construct a triangle from the lengths of its angle bisectors. Is there a more comprehensive account of ...
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### Is there any (nontrivial) constructible rational angle?

Yesterday, I talked with a friend about a problem where the solution would be an angle of $2$ radians (about $114.6°$). Then somehow the question arose whether such an angle would be constructible (...
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### Why can't we construct a square with area equal to a given equilateral triangle?

In modern geometry, given an equilateral triangle, one can't construct a square with the same area with the use of Hilbert tools. Why is this? The claim seems untrue to me, so there must be something ...
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### geometric construction of a given angle

Given any angle how can you say that it is constructable or not?
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### what name for a shape made from two intersecting circles of different sizes?

what is the name of a shape made from two circles with different radii that intersect each other? Sort of like a snowman shape, made of a big and a small ball of snow, melted together a bit! :-) ...
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### Constructing a circle through a given point, tangent to a given line, and tangent to a given circle

While browsing around about problems similar to the problem of Apollonius, I have found references to constructions of all types of circles. For example, not only is it possible to construct a circle ...
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### How to divide a pizza into $n$ parts?

Let's say you have invited $(n-1)$ people for dinner. You decide that the main course consists of one pizza for each guest, so you order $n$ pizzas. Unfortunately, the pizza guy on the scooter trips ...
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### Construction of 145 degree angle

I've tried doing it but I end up only constructing 135 degree angle.I have to use ruler without divisions and compass.It must be done with system of isosceles and equilateral triangle and their ...
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### Doubling the cube with the help of a parabola

Looking into the intersection of abstract algebra and geometry, it's well known that it is impossible to double the cube with ruler and compass, since $\sqrt[3]{2}$ is not constructible. However, I ...
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### Finding the circles passing through two points and touching a circle

Given two points and a circle, construct a/the circle through the two points and touching the given circle. I came across this problem in History of Numerical Analysis by H. Goldstein. I spent some ...
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### Motivation for studying compass and straightedge constructions? [duplicate]

Possible Duplicate: What is the (mathematical) point of geometric constructions? Are there good motivations to study compass and straightedge constructions? More specifically I want to know: 1)...
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### What is the (mathematical) point of straightedge and compass constructions?

The ancient discipline of construction by straightedge and compass is both fascinating and entertaining. But what is its significance in a mathematical sense? It is still taught in high school ...
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### Trisect unknown angle using pencil, straight edge & compass; Prove validity of technique

This question was posed by my high school geometry teacher, for extra credit: Is it possible, using only a pencil, a straightedge (not a ruler) and a compass to trisect an angle of unknown value? ...
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### What is the difference in radii of two concentric circles given an angle and length of a triangle that is inscribed in the annulus?

In relation to this geometric construction: where D is the center of both circles, if the inner radius (x = length of line segments DA and DE), the angle φ = ∠CAB, and the length Δg of line segment ...