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.

The most common use of "geometric construction" refers to the "compass and straightedge" constructions in classical Euclidean geometry. The notion has been extended also to (a) compass/straightedge constructions in non-Euclidean geometries and (b) allowing different sets of tools such as a marked straightedge (neusis) or origami.

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Proof of Construction of regular pentagon by using compass and straightedge.

How to prove that the polygon constructed by the method mentioned in the following link is indeed a regular pentagon? Constructing a Regular Pentagon (Video on YouTube)
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A conjecture about the sum of the areas of $3$ triangles built on the sides of any triangle (by means of centroid/orthocenter)

Given any triangle $\triangle ABC$, let us draw its orthocenter $D$. By means of this point, we can draw three circles with centers in $A,B,C$ and passing through $D$. These circles intersect in the points $E,F,G$, which can be seen as the vertices…
user559615
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Constructions: A straight line segment of length pi units.

A line segment of length 22/7 units or 3.14 units can be drawn. But how can a line segment be drawn of exactly pi units?
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Make a 60° angle on line $l$

We have got Line $l$ and point $P$ which is not on $l$. By using a compass and a non-graded ruler, draw a line from $P$ that makes a 60° angle with line $l$. Please help me!
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Please Prove Me Wrong (Trisection of a LINE)

I want to preface this by saying I have been trying for a while to prove myself wrong because my results appear to contradict the work of some previous work by people who have studied much more than me. Anyway. I have what I believe to be trisection…
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Construct a segment with length of $\frac{2a}{a+b^2}$

Given the following segments how would you construct a segment with length of $\frac{2a}{a+b^2}$? Given the three line segments below, of lengths a, b and 1, respectively: For example if I wanted to construct a segment $z$ satisfying an equation…
HighSchool15
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Find area of triangle ABD.

Given in $\triangle ABC,~AD$ is the angle bisector of $\angle A $. If area of $\triangle ABC = X$ , prove that area of $\triangle ABD = \dfrac{Xc}{(c+b)}.$ $a=BC$$b=AC$$c=AB$
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50 Degrees angle construction possible without protactor?

Is 50 degrees angle construction possible without a protactor or a sine table ? Only using Compass and a ruler.
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Geometric Construction : Construct a Triangle given 3 heights ..

Given 3 heights : $h_1=5\mathrm{cm}$ ; $h_2=7\mathrm{cm}$ ; $h_3=8\mathrm{cm}$ ... It is required to draw that triangle using only compass and ruler ! N.B.: It is not allowed to calculate the area then the sides: the measure of the sides won't be…
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Construct a regular hexagon of specific height?

Is it possible to construct a hexagon of particular height, meaning distance between the faces (not vertices)? I have seen various methods of constructing a hexagon (ruler and compass only) which are based on the length of a side, but have not seen…
Tyler Durden
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Given a touching circle and a tangent, find the equation of the second circle

Hi, recently I've been researching path synthesis in aircraft navigation and stumbled across a few images of constructions used to join different navigation paths together. In the image linked above, I will know the values of c,g,p1,p2&p3 and will…
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Construction of a isoceles Triangle

How can one construct an isosceles triangle with ruler and compass with the following givens the sum of the base and a side the head angle
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