# Questions tagged [geometric-transformation]

A geometric transformation is any bijection of a set having some geometric structure to itself or another such set. (from Wikipedia)

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### How to reconstruct a quadrilateral ABCD only using compass and straight edge?

Reconstruct a quadrilateral ABCD given length of its sides and the length of the midline between the first and third sides (namely all the segments drawn in the given figure) using compass and ...
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### relative transformation of coordinates on a flat surface

I have a few coordinates that form a triangle. I have a relative point to that triangle. if the coordinates get translated to a new triangle I want to calculate the new relative point. How do I do ...
156 views

### Prove that the line $XY$ goes through a fixed point where $X,Y$ are on fixed conic so that $\angle XPY = 90$ where $P$ is fixed on the conic.

Say $\mathcal{C}$ is some conic and $P\in \mathcal{C}$ is fixed point on it. For each $X$ on $\mathcal{C}$ let $Y$ be such on $\mathcal{C}$ that $\angle XPY = 90^{\circ}$. Prove that the line $XY$ ...
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### 3D Vector projection of real and imaginary part respectively and phase difference computation

I'm a bit confused regarding the phase relationship of vector components between the real and imaginary part of a complex 3D vector. I have a complex vector of an electric field (real and imaginary ...
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### Question about an elementary geometric construction

We have a circle $\Gamma$ and two points $A$, $A'$ on this circle. We have a line $\Delta$ and a point $P$ on this line: $P \in \Delta$. Do you know a way to construct points $M \in \Gamma$ such that ...
104 views

### Prove that H is orthocentre of ABC using inversion

Three equal circles pass through a given point $H$ and meet one another two by two at $A,B,C$ prove that $H$ is orthocentre of triangle $ABC$. My try - I proved it using elementary geometry methods ...
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### Calculating transformation matrix for perspective transform

I'm using the getPerspectiveTransform() method of OpenCV (description here). This method calculates a perspective transform from four pairs of the corresponding points. So we have to specify four ...
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### Find angle in triangle $ABC$ with cevian line $AD$, such that $AB=CD$.

As you can see in the picture, there is a triangle $ABC$ with $∠C=30°$ and $∠B=40°$. Now we assuming that $AB=CD$, try to find the exact value of $∠CAD$. My attempt: Denote $∠CAD$ by $x$, we know ...
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### Finding angle $x$, a geometry question

Here is the question. Find the value of $x$. I have solved this question by my own (with 3 different methods). However, all methods of mine are based on the construction of equilateral triangles.I am ...
660 views

### For regular tetrahedron $ABCD$ with center $O$, and $\overrightarrow{NO}=-3\overrightarrow{MO}$, is $NA+NB+NC+ND\geq MA+MB+MC+MD$?

Let $ABCD$ be a regular tetrahedron with center $O.$ Consider two points $M,N,$ such that $\overrightarrow{NO}=-3\overrightarrow{MO}.$ Prove or disprove that $$NA+NB+NC+ND\geq MA+MB+MC+MD$$ I ...
224 views

### Square inscribed in a right triangle problem

Let A be a point on a fixed semicircle with diameter BC. MNPQ is a square such that $M \in AB, N \in AC, P \in BC, Q \in BC$. Let D be the intersection of BN and CM and E be the center of the square. ...