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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Existence of the Square in "Squaring the Circle" Problem

I understand that a square with area $\pi$ cannot be constructed using straightedge and compass. But such a square surely exists (and can be constructed through other means), right? If I'm right, I'm confused by the Wikipedia article…
FreshAir
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Construction based on circumcenter and incenter

Construct a triangle given the exact location of its circumcenter and its incenter, and the position of its angle bisector (including its direction), but not its length. I tried to consider the angles between the points.
user198454
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smallest set of curves for constructing any real number and angle

If we are limited by what we can construct with compass and straight edge, then what are the fundamental curves required for constructing any real number? In other words, what is the smallest collection of geometric objects for constructing a line…
Honest Abe
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Circle with center point and tangential to lines

I have defined Points all points (3 blue, and one green). All points have the same distance to A point. Yellow lines are bisectors. I have equations of AB and AC with Ax + By +C = 0 form. I need construct circle (tangential to lines) with green…
m___b
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Find a point C on an infinite line AB which, when connecting two other points M and N, would form congruent angles

On an infinite line $AB$, find a point $C$ such that the rays $CM$ and $CN$ connecting $C$ with two given points $M$ and $N$ situated on the same side of $AB$ would form congruent angles with the rays $CA$ and $CB$ respectively. I think $C$ will…
hohner
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construction of the rectangle with the highest area

I have 2 times a square with side length 2, 2 times a square with side length 3, 1 times a square with side length 4 and 1 times a square with side length 5. I have to create the rectangle with the biggest area with some or all of the squares. I…
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Find circle for two points, one with given angle.

I have point A and B. I also have a vector v. How can I mathematically find a circle whose tangent at point C has the same angle as v where point C is the same as B and the circle also contains point A. Here is an illustration: Black dot is A Red…
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Trisection of an angle $ Z $ whose cosine is $ -\frac{11}{16} $ with straightedge and a compass

Suppose there exists an angle $Z$ such that $\cos Z = -\frac{11}{16}$. Prove or disprove that such an angle can be trisected with a straightedge and a compass. Well, we know that an angle is constructible if and only if its cosine is constructible.…
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Tangent Circumference Construction

"Construct a circumference that is tangent to a given circumference and tangent to a line $r$ through a point $A$ of this line." I've done the line perpendicular to $r$ through $A$, cause we know that the center of the circumference must lie in…
Ders
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Geometrical place of one point

Through one of the intersection points of two given circles, a line is build which intersects 2nd time the 2 circles in $A$ and $B$. Determine the geometrical place of the middle of $AB$. thanks for your time and help!
Akhtubir
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Construct $\sqrt{9a^2 - 4b^2}$ using compass and ruler, if $a$ and $b$ are given segments

I really don't know how to do math constructions. The problem is to construct $x$ if $a$ and $b$ are given, which means you can choose the length of them. Construct $x$: $$x = \sqrt{9a^2 - 4b^2}$$ For this construction, you need to use compasses and…
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Straight lines minimum area of triangle

Consider points P(7, 1) and O = (0, 0). If S is a point on the line y = x and T is a point on the x-axis so that P is on the line segment ST, then how to find minimum possible area of ΔOST for x coordinate of S greater than 1.
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triangle inscribed in a rectangle

given a rectangle $ABCD$ how to construct a triangle such that $\triangle X, \triangle Y$ and $\triangle Z$ have equal areas.i dont know where to start. .i tried some algebra with the area of the triangles and used pythagoras theoram to find the…
MAGNUM
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Construct any regular polygon (A003401) that has the same area as the sum of $n$ given triangles

Original question: Construct any regular geometric shape that has the same area as given triangle? A003401 ...and by construct I mean, suggest steps for construction or provide general idea My idea is application of generalized Pythagora's…
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Drawing a figure in advanced geometry.

I was not able to draw figure for a question. Question was From a point of intersection of two circles, the lines to the centers of similitude bisect the angles between the radii of the circles. Thanks in advance......
Kshitij Singh
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