Tagged Questions

For questions about properties and applications of triangles

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Question on circles…

If three circles with radii ${3}$,${4}$,${5}$ touch each other externally at points P,Q and R,then the CIRCUMRADIUS of ∆PQR is...?? My attempt i think that the let the point of the common ...
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How can I find the distance between two points within a triangle if I have the distance between each point and each vertex of the triangle?

Title says it all. It would be useful to extend the question to finding the distance if any of the points is outside of the triangle, but I'm trying to figure out the basic problem first.
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Linear algebra - Proof of a thesis concerning the height in triangles!

My Math teacher gave us some tasks we should work on. I solved most of them already, however I still could not manage to figure out the solution for this one! I would really appreciate, if someone of ...
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Prove that $\sin^2\frac{A}{2}\csc2A$, $\sin^2\frac{B}{2}\csc2B$, $\sin^2\frac{C}{2}\csc2C$ are in harmonic progression

If sides $a,b,c$ of $\triangle ABC$ are in arithmetic progression (AP), then prove that $$\sin^2\frac{A}{2}\csc2A, \quad\sin^2\frac{B}{2}\csc2B, \quad \sin^2\frac{C}{2}\csc2C$$ are in harmonic ...
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What is the length of the shorter trisector of the right angle in a $3$-$4$-$5$ triangle?

What is the length of the shorter trisector of the right angle in a $3$-$4$-$5$ triangle? I found this question in a local question paper, and I am unable to solve it. I applied Cosine formula, but ...
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Two triangles in a plane

Let $\Delta_1$ and $\Delta_2$ be two triangles in a plane with centroids $G_1$ and $G_2$ respectively. Let $X$, $Y$ be variable points on the perimeter of the triangles $\Delta_1$,$\Delta_2$ ...
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Prove that the center of a circle within a constructed triangles lies on the angle bisector

I was given steps to construct a figure: 1.) Construct a horizontal ray AB and a segment AC at an angle to the ray. Locate point D anywhere on ray AB and construct the segment CD. 2.) Construct the ...
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If three cevians are concurrent at a point and form triangles of equal area, the point is the centroid

Let D,E,F be points on side BC,CA,AB of triangle ABC. The three cevians are concurrent at a point G. The areas of triangles BGD, CGE and AGF are equal. Prove that G is the centroid of ABC I have ...
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Finding length or magnitude using vector addition and the Pythagorean theorem. I am trying to understand why vector addition and the Pythagorean theorem are giving different results? Vector ...
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Relative velocity- Finding the direction of wind.

An aircraft is flying due south at $350~\text{kmh}^{-1}$. The wind is blowing at $70~\text{kmh}^{-1}$ from the direction of $\theta$, where $\theta$ is acute. Given that the pilot is steering the ...
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Changing the side of a triangle without changing area?

$\triangle ABC$ has vertices $A=(8,2)$, $B=(0,6)$ and $C=(-3,2)$. Point $C$ can be moved along a certain line with points $A$ and $B$ remaining stationary so that the area of $ABC$ will not change? ...
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How to find the third point of a triangle in a 3D space (arm rig)

I am attempting to create a system that will replicate arm movement, so far I have mastered this in a 2D plane however I am having trouble adding the third dimension. Here is what is given, You know ...
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How do I calculate the third point of a triangle in a 3Dimensional Plane

I am attempting to create a system that will replicate arm movement, so far I have mastered this in a 2D plane however I am having trouble adding the third dimension. Here is what is given, You know ...
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How to calculate the X distance while Z object is moving top to bottom?

First of all, sorry for my extremely low knowledge about mathematics. All i am able to do is this image which describe the problem. Image of triangle + information I want to know that how can i ...
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External Bisectors of Triangle ABC

The exterior angle bisectors of $\angle B$ and $\angle C$ intersect on point $O$. $\angle BOC=70°$. Find $\angle OAC$.
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How many different ways can a circle intersect a triangle N ways?

Consider a circle intersecting a triangle. The circle and triangle can have between 0-6 total intersection points. Is there a mathematical formula for the number of possible ways they can intersect ...
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Proof to show that a quadrilateral is a paralellogram.

I am new to this site and I don't know how to code yet, so bear with me. I am trying to show that the quadrilateral ABCD in the picture below is a parallelogram. I know that since triangle EBC is ...
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Which sides of a triangle are visible to an observator?

Working o 2-d plane. Supposing that there is a observer standing on the origin (0, 0) looking to the first quadrant. If there is a triangle drawn on the first quadrant, what sides are visible to the ...
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In a triangle $ABC$ with $A=(1,3) ,B =(q,0), C =(p,-4)$ [closed]

Let $A=(1,3),B =(q,0), C =(p,-4)$, with $p>0$, the slope of $AB$ is $+45^\circ$ and $AC= \sqrt{50}$. Determine the gradient of $AB$ Calculate the equation of the line $AB$ Calculate the value of ...
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Similar triangle proof in parallelogram

Can anyone help me with this task. From the top of a parallelogram $ABCD$ lowered the vertical $AM$ and $AN$ on the lines BC and CD . Prove that triangles $\triangle ABC$ and $\triangle AMN$ similar ....
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Prove that DE || BC

Let M be the midpoint of side BC in triangle ABC. The angle bisector of BMA intersects AB in D, while the angle bisector of CMA intersects AC in E. How can i prove that DE||BC? I drew out the ...
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Is there a way of determinine the side lengths of a isosceles triangle knowing its angles and area?

I want to be able to determine the side lengths (or at least one side length) of an isosceles triangle knowing only its surface area and angles. Is this possible?
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How many different shapes can you construct with n equilateral triangles?

If you have n equilateral triangles, and you want to connect them all to each other at the edges, how many different shapes can you make? Triangles are identical in size and shapes that are ...
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what is the value of angle A

The triangle ABC is random. The line $AD$ is twice big as the line $DC$ ($AD=2*DC$). We know only the two angles that are shown in the picture. What's the value of angle $A$?
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