Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [plane-geometry]

Plane geometry is a subfield of Euclidean geometry, restricted to the flat two-dimensional space. Plane geometry studies shapes, ratios and relative locations of 2D figures which can be embedded in a 2D plane.

Plane geometry is a subfield of Euclidean geometry, restricted to the flat two-dimensional space. Plane geometry studies shapes, ratios and relative locations of 2D figures which can be embedded in a 2D plane.

1925 questions
2
votes
2 answers

Pairs of points exactly 1 unit apart in the plane

I don't have an idea how to prove, that between any n points on the plane, there are not more than $O(n^\frac{3}{2})$ pairs with distance of 1 unit between each other... Thanks a lot for any help!
Dmytro Tretiakov
  • 21
2
votes
2 answers

Finding equation of a circle

I am supposed to find an equation of a circle passing though points M(3,0,0),N(0,3,0) and P(0,0,3) I have tried to find an intersection of bisectors of lines MN and NP but ended up with nothing.
userasadfg
  • 21
  • 1
2
votes
3 answers

Two lines on a hyperplane that don't intersect or run parallel?

So that wasn't a question but a statement. At least I can't figure out how they intersect. Question is: Find an equation of the hyperplane that contains the lines q(t) = (t,t,t,1) and f(t) = (1,t,1+t,t), t $\in$ $\Re$ I need two things to answer the…
Jacob
  • 69
1
vote
1 answer

Locus of points of the incenter of right isosceles triangles

Good evening to everyone. I was trying to solve an exercise on planar geometry concerning a locus of points. More precisely, the exercise was stating : '' Suppose a line $ \varepsilon $ and a point O outside this line are fixed. We draw an…
Petros Karajan
  • 374
1
vote
2 answers

Show that the length of the hypotenuse of a right triangle is $\ge$ the length of a leg.

This question is in chapter 5 $\S$3 of Serge Lang's Basic Mathematics. Am I wrong in thinking there is no right triangle that exists such that the length of the hypotenuse is equal to the length of a leg? It seems to me that for a right triangle,…
josh h
  • 13
1
vote
1 answer

What's the measure of the angle $ \measuredangle OBH$?

For reference: In an acute triangle ABC, H is the orthocenter and O is the circumcenter. Find the $ \measuredangle OBH, if ~\measuredangle A - \measuredangle C=24^o $ My progresss: I made the drawing and the following relationships $\measuredangle…
peta arantes
  • 6,211
1
vote
1 answer

Four circles' intersections points cocircular?

In the configuration below, four circles $C_i$, $i=1,2,3,4$, are tangent as shown, and each tangent to a surrounding circle $C_0$. Q. Are the four circle intersections shown cocircular?      
Joseph O'Rourke
  • 30,327
1
vote
0 answers

Tangent of $Ax^2+By^2+2Hxy+2Gx+2Fy=0$

Need to prove that the equation of the line tangent to $Ax^2+By^2+2Hxy+2Gx+2Fy=0$ at $P(x_1,y_1)$ is $Axx_1+Byy_1+H(xy_1+yx_1)+G(x+x_1)+F(y+y_1)+C=0$ I don't know where to start.
Adrian A
  • 61
  • 5
1
vote
0 answers

$n$ amount of lines make $m$ amount of intersection points. How many values of $m$?

What I am asking is this. Given $n$ amount of lines, there are $m$ amount of intersection points. How many values of $m$ are there? Let me give an example, 5 lines in a plane. Is there a formula for this, and if so, proof?
user807252
1
vote
1 answer

Equation of plane $\pi$ crossing point $P(1,-1,2) \in \pi$. $\pi \parallel \pi_1$, $\pi_1: 3x-y+2z=0$. Present the general form and a parameter form

Calculate the equation of the plane $\pi$ crossing a given point $P(1,-1,2) \in \pi$ and such that $\pi \parallel \pi_1$, where $\pi_1: 3x-y+2z=0$. Present the normal (general) form and the parameter form. Here's what I have so…
retiredgoblin
  • 15
1
vote
3 answers

Congruence of two right triangles by equal hypothenuses and heights

Two triangles ($ABC$ and $MNP$) are right (angles $ACB$ and $MPN$ are $90$ degrees each), the hypothenuses $AB = MN$ and the heights to the hypothenuses $CD = PQ$. Prove that the two triangles are congruent.
John
  • 375
1
vote
0 answers

Prove without calculus: 2 tangent segments to convex curve longer than curve

Consider a convex curve in the plane. Let B and C be any two points on it, and let A be the intersection of the tangent to the curve at B and C. I would like to show, without calculus, that $AB + AC > BC$. With calculus, it does not seem too bad. I…
aschultz
  • 374
1
vote
1 answer

Divide a plane with $2n$ points into two equal halves

How can we divide a plane with $2n$ points into two equal halves with $n$ points each using a line?
Bilal HIMITE
  • 169
1
vote
2 answers

Distance of a plane

I have posted this question in Stack Overflow programming forum. Someone there feels it might be more suited to Mathematics. I have to warn you I am rusty in math and was terrible in Algebra. Using Accord Framework plane class. The help on this…
Eric Snyder
  • 113
1
vote
5 answers

Find $B=(x,y)$ so triangle is equilateral

Let $O=(0,0)$, $A=(3,4)$ and $B=(x,y)$ be three points in $xOy$. Find real numbers $x$ and $y$, so that $OAB$ is an equilateral triangle. I'm really struggling with this one, can someone help?
Oros Tom
  • 13
1
2
3 4 5 6 7 8