# 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.

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### Find the size of the radius of the nth circle.

In the figure shown, calculate the size of the radius of the nth circle. (Answer:$\frac{R}{n^2+2}$) I calculated the radius of the first two circles. How to extrapolate this resolution to other rays? ...
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### Unit Disks problem

Good day, I'm faced with a problem that I don't understand how to approach. I would be grateful if you could tell me at least the direction in which to think. Three circles of unit radius are given ...
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### Parallel line equation

I want to incorporate 2 diagonal lines in a logo design. The lines have to be parallel to each other and have to be exactly 0.5 inches apart when measured perpendicular. The upper point of Line 1 has ...
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### construct series of planar polygonal spirals that approximate planar curve

Let $\gamma:[a,b]\rightarrow \mathbb{R}^2$ a constant speed spiral, that is a) $\gamma$ is locally convex w.r.t. 0, that is $\gamma$ has supporting lines that locally lie above $\gamma$ and $\gamma$ ...
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### Calculate the radius of the circle that is tangent to the two others and to a line tangent to these two circles

Two circles with radii $R$ and $r$ intersect at an angle of $120°$. A common external tangent $AB$ is drawn ($A$ and $B$ are points of tangency). Calculate the size of the radius of the circle that is ...
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### Rigorous proof of ASA Congruence rule

Using Hilbert's axioms of geometry how can we prove with rigor that the angle-side-angle congruence rule is true? Most of the proofs I have seen of this seem to rely on the diagram and follow this ...
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### Calculate the $PQ$ segment in the semicircle below

In the figure, if $MN = 40$ and $NQ = 9$, Calculate $PQ$. $AB$ and $MB$ are diameters. (Answer: $21$) Note: The question does not mention whether the diameters are equal. I don't know if it would be ...
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### Converting 3d coplanar points to space of 2d plane then back into 3d

I have the equation of an arbitrary plane of the form $Ax+By+Cz+d= 0$. I also have a set of points lying on this plane, $\{p_1, p_2, ... , p_i\}$ where each $p_i$ is an $(x,y,z)$ coordinate. I would ...
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### Find the area of ​triangle ABC depending on the conditions given below

In triangle $ABC$, angle $C$ measures $120°$ and side $AC$ is greater than side $BC$. Knowing that the area of ​​the equilateral triangle with side $AB$ is $31$, the area of ​​the equilateral triangle ...
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