# Tagged Questions

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### How to embed this circle tangent to the other circles?

I want to construct a circle that would be tangent to the $3$ circles and would have its diameter lie somewhere on the segment $BI$. $EF$ includes the diameters of the $3$ given circles. $EB=BF$. ...
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### A construction of a triangle mapping with a homothety

Given an acute triangle $ABC$ draw a triangle $PQR$ such that $AB=2PQ,BC=2QR,CA=2RP$, and the lines $PQ,QR,RP$ pass through $A,B,C$ respectively. Note $A,B,C,P,Q,R$ are distinct. This is a problem ...
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### Given a pair of conics, construct (synthetically) their shared tangent lines

There are various well-known ways to construct the common tangents to a pair of circles; this is an easy one. I also just learned that we can use Pascal's Theorem to construct a tangent to a conic at ...
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### To construct a right triangle given the hypotenuse and sum of two legs [duplicate]

NOTE: I want a hint only. A compass and a straightedge construction:Given a hypotenuse and the sum of lengths of the legs,we need to construct a right triangle. MY TRY: From any ray $BE$, ,let ...
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### To draw a straight line tangent to two given ellipses

How can I draw a a straight line that touches two ellipses? There are, like for two circles, 4 different solutions. I´m not interested in the analytical solution, but in the geometrical drawing, ...
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### What are four ways to quadrisect any triangle?

What are four ways to quadrisect any triangle with compass and straightedge? I have a few already: Draw a median and from the midpoint, draw two medians to the remaining sides. Draw a median and ...
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### A problem of forming equal angles in plane geometry

C and D are two points on the same side of a straight line AB. Find a point X on AB such that angles CXA and DXB are equal.
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### Could Euclid have bisected a line segment without his method of superposition?

In Book I Proposition 10 of the Elements, Euclid performs the bisection (i.e. finding a midpoint) of a line segment. In the course of doing so, he uses Book I Proposition 4, the Side-Angle-Side ...
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### History of Compass/Straight Edge Construction

I'm interested in learning the origin of compass/straight-edge constructions. In particular, I am interested in the historical interplay between Euclid's axioms for plane geometry, and ...
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### Are there impossible boolean constructions?

I was reading about logic and I remember, for example: That with the binary $\mathtt{NAND}$ connector can be used to assemble all the other binary connectors - I already know that there are primitive ...
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### Why only compass and straightedge?

I've read and watched some lectures on euclidean geometry - not so advanced but I've seen the focus on constructions. Two instruments are used, compass and straightedge, I had the following doubts: ...
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### Drawing Euclid?

I decided to study Euclid for fun. I have Oliver Bryne's edition. I also want, as much as possible, to construct the figures myself, to get a deeper understanding. How did people traditionally do ...
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### Minimal number of moves to construct the challenges (circle packings and regular polygons) in Ancient Greek Geometry?

In the web game Ancient Greek Geometry, there are challenges to construct regular polygons and circle packings using ruler and compass constructions. The game measures the number of line and circles ...
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### Equilateral and equiangular polygon

Can we have an equilateral polygon $n \geq 5$, which is not equiangular? Ot does every odd n-gon which is equilateral must be equiangular? Is a construction of an equilateral but not equiangular n-gon ...
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### Are the lengths from this recursive construction a geometric sequence?

In his 1999 review of Edward Tufte's Visual Explanations in the Notices of the AMS (third page), Bill Casselman gives a very pretty proof of the irrationality of the golden mean. More precisely, ...
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### Construction of a triangle, given: side, sum of the other sides and angle between them.

Given: $\overline{AB}$, $\overline{AC}+\overline{BC}$ and $\angle C$. Construct the triangle $\triangle ABC$ using rule and compass.
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### Sangaku. How to draw those three circles with only a ruler and a compass?

I found in a book of Sangakus the following problem. Let $R_b$, $R_g$ and $R_r$ the radiuses of the blue, green and red circles $C_b$, $C_g$ and $C_r$. Prove that ...
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### Construct two chords of equal length through points A and B (two arbitrary points INSIDE a circle) that are perpendicular to each other.

Its a construction problem I am having trouble with. I realize I need to use rotations and/or other isometries but I am really stuck. Any help would be really appreciated! Thanks!
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### Construct tangent to a circle

Using a ruler and a compass how can construct a line through a point and tangent to a circle. What I don't want is to eyeball the line by trying to line-up the ruler over the circle. Best if I could ...
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### Constructing $\sqrt{a}$ for a constructable $0\leq a\in\mathbb{R}$ - Compass and straightedge constructions [duplicate]

Possible Duplicate: Compass-and-straightedge construction of the square root of a given line? I wish to understand how to construct $\sqrt{a}$ for a constructable $0\leq a\in\mathbb{R}$ , ...
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### Geometrical construction of the product on $\mathbb R$ [duplicate]

Possible Duplicate: Representing the multiplication of two numbers on the real line Consider the real line in the plane. Suppose you are given the location of the point associated to $0$ ...
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### Having two points of a square and only a compass, how to find the remaining two?

I remember being presented a mathematical puzzle some years back that I still can't solve. The problem is defined as follows: We have two points on a plane, and using only a compass, how do we find ...
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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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### Sangaku: Show line segment is perpendicular to diameter of container circle

"From a 1803 Sangaku found in Gumma Prefecture. The base of an isosceles triangle sits on a diameter of the large circle. This diameter also bisects the circle on the left, which is inscribed so that ...
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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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### geometric construction of a given angle

Given any angle how can you say that it is constructable or not?
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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 ...