Mathematics Stack Exchange
Mathematics Stack Exchange

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.

1013 questions
1
vote
1 answer

Proving there is a rectangle inside an hexagone.

How can I prove this : Let a regular hexagon ABCDEF and M, N, R and S the respective midpoints of AB, CD, DE and FA: i) Prove that the MNRS is a rectangle. ii) compare the area of MNRS and the area of ​​the hexagon My ideas For the first question, I…
Justin D.
  • 745
1
vote
1 answer

Construction of another regular pentagon

I have a problem that involves construction with the ruler and compass. I want to prove more constructions of the regular pentagon. I finished demonstrating some more constructions, but I couldn’t do one of them. Here is the problem: considering the…
Michael
  • 39
1
vote
1 answer

Construction of 3 circles touching each other externally.

The context is construction of three circles with different radii so that they touch each other externally using a graduated ruler and a compass. I have done it by drawing a triangle where each side is the sum of the radii of distinct combination of…
MrAP
  • 3,003
1
vote
2 answers

Construct two circular arcs meeting at a common point

Suppose we are given a ray $\rho_a$ beginning at point $a$ and a ray $\rho_b$ beginning at point $b$. I want to find a circle $C_a$ tangent to $\rho_a$ at point $a$ and another circle $C_b$ tangent to $\rho_b$ at point $b$ such that there exists…
Joe
  • 631
1
vote
2 answers

Construction of harmonic mean with ruler and compass

Exercise 8.10 at this site http://www.euclidea.xyz/ claims that harmonic mean can be built with just 4 simple objects (lines and/or circles) My best result is 6 objects (including perpendiculars and segment bisector). Do you have any hint to…
Raffaele
  • 26,371
1
vote
2 answers

Construct circle center from chord

Is it possible to construct the center of a circle from a single chord? If I construct the perpendicular bisector of the chord and then construct the perpendicular bisector of that, wouldn't the exact point of intersection be the center of the…
Lundborg
  • 1,646
1
vote
1 answer

How can we construct the incenter of a triangle using a compass alone?

To clarify, you have 3 non-collinear points $A$, $B$, and $C$. You have to get the incenter of the triangle $ABC$ using only a compass. Has it been solved/Is it possible? (No straight edge)
NameNotFoundException
  • 69
  • 6
1
vote
2 answers

Ruler and compass question

Provide the exact list of steps needed to draw, using ruler and compass, a line $M$ through a given point $A$ and parallel to a given line $L$ (given by two points $B$ and $C$ on it). Assume that $A$ is not on $L$. I am completely new to this. So…
snowman
  • 3,733
  • 8
  • 42
  • 73
1
vote
1 answer

Accuracy of a Construction

Is there an easy way to find the accuracy of a construction given a straight-edge and compass? For instance setting the point of a compass on an existing line. How do I know how exact that is? Or more critical, putting the compass on "the point"…
Allyn Shell
  • 47
1
vote
1 answer

Construct circle tangent to two lines

Given two line segments $ab$ and $cd$, I want to draw a circle tangent to both line segments and passing through points $c$ and $b$. Primitive operations available to me are: Draw a line between two points. Draw a perpendicular line passing…
Joe
  • 631
1
vote
1 answer

Given a $\triangle ABC$ construct another triangle with sides measuring the inverses of the altitudes of $\triangle ABC$

Given a $\triangle ABC$, we want to construct the $\triangle XYZ$ whose sides are the inverses of the altitudes of $\triangle ABC$ . If we denote the altitudes by $h_a,h_b,h_c$ then the sides of $\triangle XYZ$ are…
onlyme
  • 1,397
0
votes
0 answers

Geometric question (middle line of a parallelogram)

Let $ABCD$ be a parallelogram and $I,J$ are two points such that $AI = ID$ and $BJ = JD$. Show that ($IJ$) is parallel to ($AB$).
shao
  • 1
0
votes
0 answers

proof of construction of angle 360/17

One construction for a 17-sided polygon is shown below. Construct a circle with diameter and radius OC perpendicular to AOB Construct OD = OC/4 Construct DA Bisect angle ODA twice to construct angle ODE (= ODA/4) Construct angle EDF = 45…
Satvik Mashkaria
  • 3,636
  • 3
  • 19
  • 37
0
votes
2 answers

Construction by compass and straightedge.

l,m,n are three concurrent line concurrent at point A. Given a point B on line l. Is it possible to construct point C on line n such that line m is a median of triangle ABC
Satvik Mashkaria
  • 29
0
votes
2 answers

How can I construct a circle given these conditions?

Given the angle $∠pOq$ and point $M$, which is not on the ray $p$. Construct a circle with its center on line $q$ that passes through point $M$ and touches line $p$. If I mark the point of tangency on line p as D, and the center of the circle on…
cchris
  • 3
1 2 3 4
5
6 7 8