# geometry's questions - English 1answer

28.550 geometry questions.

### 2 Concyclic points on a circle

This is a question I met in some notes. I need some help here. Let $ABC$ be an acute triangle and let $AA_1, BB_1, CC_1$ be its altitudes. Segments $AA_1$ and $B_1C_1$ meet at $K$. The ...

### Find area of cross and shaded area in a circle

4 answers, 577 views geometry circle area
I need to find the area of the shaded (grey) region in the above picture. All sides of the cross are 4. I feel like this question has an easy answer, but I cannot seem to figure it out. I tried to ...

### Large convex polygons in almost convex sets

0 answers, 9 views combinatorics geometry
The Erdos-Szekeres theorem (happy ending problem) says that among any $n$ points in general position in $\mathbb{R}^2$, there are $\Omega(\log n)$ points in convex position. There are also ...

### Fix points and invariant planes of projectivity not using coordinates

Let $A,B,C,D \in \mathbb{RP}^2$ be a quadrivertex. Let $f: \mathbb{RP}^2 \to \mathbb{RP}^2, A\mapsto B, B \mapsto C, C \mapsto D, D \mapsto A$. Find the fix points and invariant planes of $f$ and ...

### Find the angle at which two right circular cone resting on curved surface, touch each other

1 answers, 40 views geometry angle
Two identical right circular cones are resting on their curved surface as shown in the second row of the image above. Let V be the top vertex and O (O') be the center of base circles and A(A') be the ...

### 2 How did the ancient Greeks discover formulas for volume and surface area?

2 answers, 690 views geometry soft-question math-history
How did the ancient Greeks discover formulas for volume and surface area of different objects, e.g. of a sphere? They did not know about integrals, so there must another way?

### Rotation of a square/rectangle around a point

3 answers, 1.026 views geometry rotations plane-geometry
this is the first time I ask a question here. I want to know what's the simplest way of calculating the coordinates for the 4 points of a square/rectangle on a plane, after a rotation around a point, ...

### 4 Using Menelaus to show: The perpendicular bisectors of the angles bisectors of a triangle meet opposite sides in collinear points

1 answers, 63 views geometry euclidean-geometry triangle
Prove that the perpendicular bisectors of the interior angle bisectors of any triangle meet the sides opposite the angles being bisected in three collinear points. Here is what I have so far. ...

### 1 Using the Properties of Similar triangles and angle properties to find the length AC

1 answers, 16 views geometry modular-arithmetic angle
Find the length of AC What i tried Since the diagram is a trapezoid, angle $DAB$ is $180-140=40$ degrees. Then using the properties of simillar triangles, angle $DAC$ is equal to angle $CAB$,thus ...

### 1 Find a segment length in geometric problem (figure provided).

1 answers, 27 views geometry contest-math
Given: the situation described in the figure below, with $\alpha=45^\circ$, $\overline{AS}=12$, $\overline{DS}=6$. Find: $\overline{QS}$. Question from a math contest. I've tried some ideas but ...

### -2 Which of the statements, with respect to the triangle, is correct?

The answer should be I) and II), but I have only been able to solve II). It is supposed that I must solve this only with knowledge of secondary elements of the triangle and criteria of congruence of ...

### How to connect 9 dots with 4 straight lines?

The segments can also cut each other. I have tried and tried but I can do it with 5 segments only.

### 1 How is this geometrical invariant called in English?

I am studying affine and projective geometry and I have encountered some invariant: the cross ratio, which in Italia is called "birapporto" and another one which I do not know the name of in English. ...

### 1 Perimeter of a finite set formula - isoperimeter inequality

Next year I will be embarking on a dissertation on isoperimetric inequalities; I'm doing some initial research and I am frequently coming across the definition; Let $\Omega$ be an open set in $R^n$. ...

### -3 Do line equations exist in which it is impossible to find a parallel? [on hold]

I cannot conceive of any possible way this could occur, dDo any of these kind of lines exist?

### The relative position of a plane and a line in the real affine space $\Bbb A^4$

In the real affine space $\Bbb A^4$ consider the plane $\pi$ defined by $$\begin{cases}x-y+w-1=0 \\ x-2y+z+1=0 \end{cases}$$and the line $r_k$ that goes through $P=(1,0,3,1)$ and $Q_k=(2k,k,3k,2k)$, ...

### Prove that the triangle inscribed inside a circle has the largest area geometrically.(Without calculus) [on hold]

Prove that the triangle inscribed inside a circle has the largest area geometrically.(Without calculus). How can i explain this to a class 6 child.

### 3 is difference of radius of 2 circles is not depend upon their perimeter

1 answers, 58 views geometry circle puzzle
I read on the Internet it's true, but I suspect it: Take a ribbon tightly wound around the equator of the earth. Add 1 meter to that ribbon by cutting it at any point. Uniformly lift above the earth, ...

### Surface area using Integration [duplicate]

0 answers, 32 views integration geometry
Probably really dumb question but here it goes. We know Volume of solid formed by rotating $f(x)$ along x-axis is given by $$V=\pi\int_a^b(f(x))^2dx$$ Which is derived by adding surface area of ...

### Find the area of the rhombus given its side length and sum of diagonals

How can we find the area of the rhombus with side length $a=5$ and sum of diagonals $d_1+d_2=14$. I know two formulas for the area of rhombus ($h$ stands for height): $$A=ah=\frac{d_1d_2}{2}$$ But I ...

### 2 Vectors (GCSE/High school)

1 answers, 26 views geometry vectors
Hi, I'm struggling to complete this question. I am required to find vectors $\vec{ED}$ and $\vec{EF}$ in terms of a and b. I have so far found that vector $\vec{ED}$ = b - $\frac{5}{3}$a. I would ...

### 3 What is the area of the shaded region in terms of $n$?

1 answers, 65 views geometry trigonometry

### Common Conjugate Diameters of Conics

Find the equation to the common conjugate diameters of the conics $x^2+4xy+6y^2=1$ and $6x^2+6xy+9y^2=1$. I dont know how to start here.

### Geometry, Quaternions, Rotations

1 answers, 34 views geometry rotations quaternions
For a coordinate system $C_2$, if I have the angles made by its coordinate axes ($x_2$,$y_2$ and $z_2$) with the coordinate axes($x_1$, $y_1$ and $z_1$) respectively of another coordinate system $C_1$,...

### A geometry problem asking to prove point of intersection of $2$ cevians lies on circumcircle of the triangle.

2 answers, 55 views geometry triangle
The points $P$ and $Q$ are chosen on the side $BC$ of an $acute$$angled$- $triangleABC$ so that $\angle PAB=\angle ACB$ and $\angle QAC=\angle CBA$. The points $M$ and $N$ are taken on the rays $AP$ ...

1 answers, 89 views geometry puzzle area
I recently saw a similar problem online but found the area in a completely different way. Problem: There is a unit square, i.e. a square with side length equal to $\text 1$. Two lines are placed ...

### Why circle is equal to 360 degrees? [duplicate]

A circle is divided into 360 little parts called degrees. Why or how did they choose that figure? Is there a very strong reason for that or it just a accidentally choose.

### 1 Complex Analysis: Transformations and Equation Solutions

2 answers, 18 views complex-analysis geometry analysis
This might be an odd question, but I recently spent a very long time solving a problem in Gamelin's Complex Analysis and I wanted to understand exactly what was making it so difficult for me. ...

### Plane fitting using svd

1 answers, 2.657 views geometry interpolation svd
I am trying to get a best fit plane in a 3d space of points. I am using an svd as described in https://stackoverflow.com/questions/10900141/fast-plane-fitting-to-many-points. If I use the data ...