# Tagged Questions

For questions about geometric shapes, congruences, similarities, transformations, as well as the properties of classes of figures, points, lines, angles.

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### Sum of angles in a polygon - Alternative solution

I was fascinated by this problem from the first moment I saw it. Let $P$ be a convex polygon which has no two sides which are parallel. Each side $A_iA_{i+1}$ has a furthest away point $C_i$. ...
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### Construct point P 4.2cm from A and 5.6cm from B

A and B are 2 points 7cm apart. Construct the positions of point P which is 4.2cm from A and B 5.6cm from B. How many possible positions for P are there. Measure the distance between them.
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### Geometry Parabola $2x^2+\alpha x+3\alpha$ to find common point

Can you help me find the answer to this question? For any real number $\alpha$, the parabola $f_{\alpha}(x) = 2x^2 + \alpha x + 3\alpha$ passes through the common point $(a, b)$. What is the value ...
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### Curvature on topological spaces

On what subsets of the category of topological spaces are different notions of curvature defined?
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### a problem of Geometry

in Tetrahedral ABCD : E,F and G are to order Middle of sides AB , BC, AD . also GE is Perpendicular to AB and GF is Perpendicular to BC . if angle of ABC is 96 degree . calculate angle of ACD?
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### Parabolas and projectiles

Given $2$ points, $A$ and $B$, if I am in $A$ and I have an inclination angle $c$, with how many velocity do I need to shoot a projectile to hit $B$ ? My problem is, how do I setup this data in an ...
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### How to model bending, folding of 2D figures?

2D shape can be folded in various ways. For example, trapezoid can have its sides (with the acute angles) folded, so that it will effectively become rectangle – with the difference, that part of the ...
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### I have a vector of length 1, and two angles (in $xz$ plane and $yz$ plane), how do i get the $x,y,z$ compontents of this vector?

I just can't see what's wrong, this should be relatively simple... I have a vector which has length 1. Then, I have two angles. The first ($\gamma$) is the angle between the projection of the vector ...
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### Triangle in hexagon

In a regular hexagon ABCDEF is the midpoint (G)of the sides FE and S intersection of lines AC and GB. (a) What is the relationship shared point of straight ...
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### Finding An Equation For A Parabola

The information given in this particular problem: Axis is parallel to y-axis; graph passes through and $(4,11)$.$(3, 4)$ $(0,3)$ From this information, I know that it opens either upwards or ...
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### Can it be argued that this question only has 1 answer ultimately?

I came across this quiz question in a forum today. I would like to ask for your opinion of this notorious mathematics question, and also, to share. This question came out in Singapore's PSLE ...
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### Is there a way to derive the surface of a ball without integral? [duplicate]

Possible Duplicate: Can the Surface Area of a Sphere be found without using Integration? A ball is effectively a pyramid with "curved" based. If we know the surface, which is $O=4 \pi r^2$, ...
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### What are spatial Transformations?

What are spatial Transformations? Are Affine transformations also part of spatial transformations?
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### What is the maximum number of regions produced, i.e. $f(n)$, by joining all vertexes with line segments of a convex polygon with $n$ sides?

What is the maximum number of regions produced, i.e. $f(n)$, by joining all vertexes with line segments of a convex polygon with $n$ sides? For example, for the hexagon on the left, number of ...
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### Determine whether the triangles $ABC$ and $DEF$ are rectangles

How can we determine whether the triangles $ABC$ and $DEF$ are rectangles? We have $A(-6,5),B(-3,3),C(1,9),D(1,3),E(5,1),F(11,10)$.
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### finding area of the fourth circle

Three circles of the same radius are arranged in such way that one circle is tangent to the other two. A fourth circle is drawn so that it will contain three circles and be tangent to the other ...
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### Why does this system of equations result in an always-positive output?

I have two variables, M and P, whose relationship is described by the following two equations: [1] P = 50.5 * M / ( M - 50) [2] M = C * P where C is a positive ...