# Tagged Questions

geometry assuming the parallel postulate of Euclid: in a plane, given a line and a point not on that line, there is exactly one line parallel to the given line through the given point.

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### Construct parallel through a triangle satisfying a sum condition

I would like to draw, using the classical compass and rule methods, some points $D$ and $E$ given a triangle $\Delta ABC$ such that $BD + EC = DE$ and $DE$ is parallel to $BC$, as in the following ...
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### Question: What theorem should I use for this geometry problem.

I have already solved this problem using trig, however I feel that their must be an easier way to solve this problem using some theorem or property of quadrilaterals that I am forgetting. Initially ...
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### A simple proof that a polygon circumscribing a circle overestimates its perimeter

Looking at the picture below, it's easy to see why the perimeter of a polygon inscribed in a circle is an underestimation of the circle's perimeter. This follows from the triangle inequality: Any side ...
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### Euclidean Geometry Equilateral Triangle Problem

ABC is a equilateral triangle with vertex A fixed and B moving in a given straight line. Find the locus of C. Though it is clear that being an equilateral triangle, the size of the triangle must ...
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### Is it true that: $\| a \| \| b \| \cos \alpha = \langle a,b\rangle$ [closed]

Let $a , b \in \mathbb{R}^n$ and let $\alpha$ be the angle formed between $a$ and $b$. Is it true that: $$\| a \| \| b \| \cos \alpha = \langle a,b\rangle$$ ($\langle\cdot,\cdot\rangle$ being the ...
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### How do i compute the closest points on a sphere given a point outside the sphere?

I looking for method which can compute the yellow area in this image.. The ball with the green fill is a sphere, where i know the center point and the radius of it. The circle with the red fill ...
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### Distance between two lines

Find the distance between the lines $l_1:$ $x=1+4t,y=5-4t,z=-1+5t$ and $l_2:x=2+8t,y=4-3t,z=5+t$ So the approach in general is to find a vector that is orthogonal to 2 planes that the lines are in ...