# Questions tagged [synthetic-geometry]

Questions on using GeometricScene, GeometricAssertion, RandomInstance, and FindGeometricConjectures.

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### How to solve a geometric problem about a triangle using GeometricSolveValues?

I try to solve not so difficult geometric problem from an exercise book on elementary math with 14.0 on Windows 10: Let a triangle $\triangle ABC$ be given and the area of $\triangle ABC$ be equal to ...
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1 vote
72 views

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### How to construct the Nagel point of a triangle with GeometricScene?

Let us consider the Nagel point of a triangle. According to this article,"There exists an easy construction of the Nagel point. Starting from each vertex of a triangle, it suffices to carry twice ...
• 25.7k
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### How to plot Morley triangle by Synthetic Geometry method?

As the Wiki The three points of intersection of the adjacent angle trisectors form an equilateral triangle, called the Morley triangle So I write this code: ...
• 26.5k
1 vote
71 views

### RandomInstance of GeometricScene producing unexpected result

Consider the following scene as an example: ...
• 9,293
61 views

### GeometricScene extremely slow or cannot complete

I would like to find instances of the following dodecahedral wheel generalized to the situation where the red squares become rhombuses. I tried this using RandomInstance[GeometricScene], but ...
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### GeometricScene is slow and does not find an answer to a visually obvious problem for many points

I'm trying to use GeometricScene to visualize a finite patch of a periodic tiling of triangles and rhombi. When I require the rhombi to be squares (using "Regular" property on the Polygons),...
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### Can I make RandomInstance use exact arithmetic?

When using RandomInstance on a GeometricScene the answer loses precision when root objects are encountered. Is there a way to ...
• 9,293
1 vote
162 views

### Locating the intersections of two circles in a GeometricScene where the points are symbolic

I'm trying to intersect two circles in a GeometricScene. ...
• 343
113 views

### How to define the intersection of two lines as a point

I tried the code below (I sort of translated it from written notation), where I hoped that [Intersection] would give me the intersection of line ac with the altitude from b: ...
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### How to deduce circle theorems in Wolfram language?

I can deduce the first one by applying FindGeometricConjectures on the following scene: ...
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### Intersection of 3 circles in GeometricScene

I am trying to represent the image below in Mathematica and can't seem to make it work. There doesn't seem to be any constraint of type circle intersection in the documentation. I tried this: ...
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### How can I calculate the ratio of the line segments in the following geometric scene?

The following code can draw the corresponding geometric scene. By observing for many times, we can know that the length ratio of line CE and line ...
### How to calculate the degree of $∠FEB$ under this geometric scene
I want to calculate the $∠FEB$ in the figure below, but I can't solve this question with GeometricScene function. What can I do to find the answers to these ...