# Questions tagged [triangles]

For questions about properties and applications of triangles.

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### Let the triangle $ABC$ be $\angle A = 110°$ and $\angle B = 40°$. We consider a point $E$ . Show that $CA=CE$

QUESTION Let the triangle $ABC$ be $\angle A = 110°$ and $\angle B = 40°$. We consider a point $E$ inside the triangle $ABC$ so that $\angle ECB = 10°$ and $\angle EBC=20°$. Show that $CA=CE$. my ...
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### Can two triangles not be congruent but five elements in triangle are same

Can two triangles not be congruent but five elements in triangle are same
1 vote
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### How to show that two certain chords of a circle passing through the incentre of a given triangle are equal?

Let $I$ be the incenter of a triangle $\triangle ABC$. The circle $AIB$ meets the sides $BC$ and $AC$ at points $M$ and $N$, respectively. I'm trying to prove then that $BM=AN$. Here's a figure for ...
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### How were the $x$ and $y$ coordinates of intersecting point calculated?

Right angled triangle at $(0,0) (0,100)$ and $(200,0)$ Came across the solution of this in my coding and the co-ordinates of intersecting point of hypotenuse and line passing through origin and user ...
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### A Trigonometric Inequality in a triangle. [closed]

Prove that in any acute $\Delta ABC,$ $$\sin A \sin B + \sin B \sin C + \sin C \sin A \geq (1 + \sqrt{2\cos A \cos B \cos C})^2.$$
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### How to find length of side of smaller scalene triangle inside larger scalene triangle

I'm dealing with a real-world problem that can be abstracted into triangles. The knowns are: length of $AB$ length of $CB$ length of $AC$ length of $EF$ $EF$ and $AC$ are parallel In other words, ...
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### A problem about a right triangle and a circle [closed]

On the hypotenuse AB of right triangle ABC the altitude CH is drawn. The perpendiculars HK and HE are drawn from the point H to the cathetes (K in AC and E in CB). Find the radius of the circle in ...
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### The area of a triangle using sine

Please tell me why this statement is true for triangles with an obtuse angle, acute angle and the same two sides a and b: ...
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### Proving two triangles congruent given two congruent sides and a congruent median

The title was a bit too short for me to fit the full details, so here's the scenario I have. Prove that two triangles are congruent if in two triangles, the median from the common vertex and two sides ...
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### The ratio of the volume of a pyramid when it is divided into two halves

Let's assume we have a pyramid with a multi-dimensional triangular cross-section. If the dimension is equal to 2, it becomes a triangle. Now, if we divide the pyramid (or the triangle in two ...
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### A "New" Special Point in a Triangle.

I was playing with the software Geometry Expressions and I was exploring generalizations of special points in triangles (centroid, orthocenters, etc.) when I stumbled upon this construction. J is ...
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### Area of non-right angleTriangle is given, rise/run given, no sidelength is known, calculate triangle height.

I have a triangle of $600m^2$ area, I do not have any lengths of this triangle, I only have the rise/run of both sides that are not sitting on the x-axis, and the area, can I find the height given ...
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### How many unique triangles of the same type can fit in a circle? [closed]

Given a circle of any radius, i want to find how many unique triangles of the same shape can fit in that circle. All the three vertices of every triangle have to be on the perimeter of that circle. ...
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### Finding the angle EDB in triangle ABC, where E is the intersection of the angle bisector of C with side AB and D is a point on BC

This was a question I encountered while looking at some weekly math questions my school had hung in front of the department last week: I was unable to solve it, and now that some time has passed, I'd ...
1 vote
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### Equality of Segments in a Corner with Two Tangent Inscribed Circles

The problem Two circles are inscribed in the corner. Points $A$ and $B$ are points of contact of the first circle with the sides of the angle, points $A_{1}$ and $B_{1}$ are points of contact of the ...
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### Finding Value $q$ in a Triangle Given: Base $c$, Height $hc$, and Angle $γ$

The objective is to determine the value $q$ for a specific angle $γ$. Given is a triangle with the known values: base length $c$, height $hc$ relative to this base, the angle $γ$ opposite this base. ...
1 vote
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### Vertex circle radii of Pythagorean triples

@Blue was kind with his comments on a previous question here. I'd now like to share some new relationships I found using algegra and my favorite formula for generating Pythagorean triples. In this ...
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### Proving that no tile can fill both squares and equilateral triangles

Cut up a square into a finite number of identical tiles. Here is one possibility: How do I prove that the tiles could never be rearranged to form an equilateral triangle (with filled interior and no ...
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### Showing that the centers of two semicircles and a circle inscribed in a quarter circle form a right triangle

The challenge in this image is to determine the radii of the two semicircles and the full circle. Determining the radii of the two semicircles is straightforward; if the radius of the quarter circle ...
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### Which formula does it use here to get the curvature?

I'm reading the wikipedia page https://en.m.wikipedia.org/wiki/Menger_curvature It mensions a so-called well-known formula here but doesn't mention its name. I guess it is heron's formula. But again ...
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1 vote