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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
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The intersection point of bisector of a pyramid

Under which conditions there is an intersection point for all bisectors of a pyramid? A bisector of a pyramid initiating from a vertex is a line which has the same angle with all edges who are neighbor of that vertex.(A natural…
Ali Taghavi
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Can a plane be perpendicular in two other planes if those planes are not parallel to each other?

I have to write equation of a plane which passes through a point and its perpendicular to 2 planes , but before I start solving I was thinking if can a plane be perpendicular to two other planes , if those 2 others are not parallel to each other (…
Johnny Adams
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How can I tell if a vector is normal (orthogonal) to the plane?

I have to write equation of plane given 2 points $A=(-5,4,2)$ and $B(-3,2,-1)$ and vector $u=(1,2,-3)$. What I did was get a vector from points $A$ and $B$ , $AB=(2,-2,-3)$ and then I found cross product between $AB$ and $u$, $n= AB \times u =…
Johnny Adams
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intersection of 3 planes

Let $P_1$, $P_2$ and $P_3$ denote, respectively, the planes defined by $$a_1 x+b_1 y+c_1 z= \alpha_1$$ $$a_2 x+b_2 y+c_2 z= \alpha_2$$ $$a_3 x+b_3 y+c_3 z= \alpha_3$$ It is given that $P_1$, $P_2$ and $P_3$ intersect exactly at one point when…
Gopesh Thakur
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$\angle ABC = \angle AKC = 90^\circ$, Find length of $BK$.

Diagonal $AC$ of square $ABCD$ coincides with the hypotenuse of right triangle $ACK$. Assuming $B,K$ lie on the same side of $AC$, Prove the following - $BK = \frac{\left| AK - CK \right|}{\sqrt{2}}$ $DK = \frac{\left| AK + CK \right|}{\sqrt{2}}$…
Rezwan Arefin
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Question about proof of Manhattan Minimal Spanning Tree

In this tutorial about line sweep algorithms, there is a section for minimal spanning tree. There is a part that says:- The figure shows the situation in just one of the octants, the West-Northwest one. Q is the closest neighbour (with the dashed…
Cerberus
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Equality and existence proof of a point in a triangle and its areas

Can we always find a point $F$ in the line $BC$ of any triangle such as above so that the triangle $APQ$ is an isosceles triangle and the area of the triangle $AreaAPQ=AreaABC$? It'll be grateful if someone could help me with this. Given $AF$ is…
Jyotishraj Thoudam
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A geometry problem based on circles.

Question:- Consider three equal circles $S_1$, $S_2$, and $S_3$ each of which passes through a given point $H$. Other than that, $S_1$ and $S_2$ intersect at $A$, $S_2$ and $S_3$ intersect at $B$, $S_3$ and $S_1$ intersect at $C$. Show that $H$ is…
Mriganka Parasar
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Given a plane equation (ax+by+cz=d), how does one find a point on the plane (x0, y0,z0)?

Given a plane equation in the form ax+by+cz=d, how can one find the point (x0, y0, z0)? I already know what the a,b,c,d coeffiecients are. I am not referring to the x,y,z intercepts ie. d=-ax0-by0-cz0 See the example here on…
math_Artist88
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Plane Geometry: unit square and traced ray from vertex

The problem: unit square, ABCD. Extend AB as a Ray and trace a Ray from D, crossing the side BC at E and the Ray AB at F. EF = 1. What is the length of BE? (Image attached to scale) Contructed problem to scale This problem is "easy" to…
J.P.
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Longest and Shortest Medians

Is it true for every triangle that the longest median is to the shortest side and the shortest median is to the longest side?
Sekhar0210
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Coordinate geometry dividing the plane by pairwise straight line

Three pairwise straight line intersecting (but not at the same point) by how many parts these lines divides the plane?
Imran Rashid
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How to transform plane equation

I have the following mapping from R3 -> R3: Vector3 f(Vector3 v) { // Only points with |x| < z and |y| < z and 0 < z <= SomeConstant are of interest assert(abs(v.x) <= v.z); assert(abs(v.y) <= v.z); assert(v.z > 0); assert(v.z <=…
matthias_buehlmann
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What's the value of the segment $MN$ in the figure below?

For refrence: In the figure shown: H ➔ Orthocenter of $\triangle$ ABC; also: BH = 16, AC = 30 and BN = NC Find: MN An important property that can be useful: $OG = 2BH \therefore BH = 8$ Tracing the circumference circumscribed to the triangle…
peta arantes
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Predict Collision Between 2 Uniform Circular Motion Objects

this is my first question on the forum and my algebra is rusty so please be indulgent ^^' I want to predict collision between two uniform circular motion objects for which i know velocity (angular speed in radian), distance from the origin (radius),…
despe
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