# Tagged Questions

For questions about properties and applications of triangles

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### Circle Geometry - What Information Given can help me find the other angles. [closed]

I'm currently studying for a test in Grade 8 Honours Math (Grade 9). We have some questions involving Circle Geometry, but I'm having trouble here: You see, I know the value of w due to it being an ...
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### The geometric construction of the $90^\circ, 87^\circ, 3^\circ$ triangle

The construction of the $90^\circ, 45^\circ, 45^\circ$ and the $90^\circ, 60^\circ, 30^\circ$ triangles is well known. How can be constructed a triangle with angles $90^\circ, 87^\circ, 3^\circ$ ...
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### find $c$ and $b$ in terms of $x$ and $a$

I have this geometry problem. Supose any $\triangle{ABC}$, where $\overline{CE} \perp \overline{AB}$; $\overline{CM}$ is median; $n$ is $proy_{\overline{CM}}\overline{AB}$; $\angle{CMA}$ is obtuse....
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### Area of triangle constructed from the medians of other triangle

We have triangle ABC of area P. Is it possible to compute the area of a triangle with sides "made" from medians of the triangle ABC in terms of P I'm looking for some hints maybe,
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### right-angled triangle problem

If the hypotenuse is 8 cm, one of the sides is X cm and the other 4 cm longer how do i find the two unknown sides? I started by applying the Pythagorean theorem like this $x^2+(4x)^2=8^2$ but i don't ...
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### Geometry problem on angle bisectors and intersecting line segments

Two equal line segments $AB$ and $CD$ intersect each other at a point $M$. If the perpendicular bisectors of $AD$ and $BC$ intersect each other at the point $N$, prove that the two angles $\angle AMN$ ...
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### Making bigger penny triangles from smaller

I thought up a problem a long time ago, and googling doesn't even close to turn up the answer. It is this: Given unlimited 3-penny triangles (e.g. triangles with 3 pennies touching each other,) for ...
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### Prove that Triangle ABC is an equilateral triangle iff $\tan{A}+\tan{B}+\tan{C} = 3^\frac32$.

This question is picked from AM GM HM inequalities, so this is to be proved form that concept only, I think it isn't possible because there is no inequality, but if it is please tell me how.
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### Is these angles 90 degrees?

If I have the following triangle: Where $\angle B=\angle C = O$ And $AP$ bisects $\angle A$ so essentially $\angle BAP = \angle CAP = \frac12 \angle A$ We can prove that $\angle APB = \angle APC$ but ...
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### Given a right triangle's perimeter and difference between median and height to the hypotenuse, find it's area.

I have been trying to solve the following problem for a while: You are given a right triangle ABC (angle C is right). The perimeter ABC is 72. CK is the median, and CM is the height to the hypotenuse....
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### The value of $(a+b)$, according to the question.

My friend gave me a question I tried my best, but I'm low on triangle concept. Points $O, A, B, C...$ are shown in the figure where $OA=2AB=4BC=...$ and so on. Let $A$ be the centroid of a ...
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### Exponent analog to the factorial function

Triangular numbers can be discovered by taking any number $n$, and adding $$\sum_{i=0}^n i = n + (n - 1) + (n - 2) ... 1 = \frac{n(n + 1)}{2}$$ These numbers can be generalized by putting any real ...
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### How to find area of isosceles triangle when given two heights? [closed]

So I know the sine and cosine theorem and I tried using them but I got nowhere. (I got to an equation which I can't solve and I know there must be an easier method since we have not studied how to ...
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### Find coordinates of point C in a equilateral triangle [closed]

How to find the coordinates of point C in a equilateral triangle, where $A=(-2,2)$ and $B=(6,2)$. http://i.stack.imgur.com/TXjjG.png Thanks in advance
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### Euclidean Geometry Equilateral Triangle Problem

ABC is a equilateral triangle with vertex A fixed and B moving in a given straight line. Find the locus of C. Though it is clear that being an equilateral triangle, the size of the triangle must ...
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### Sum of the length of the perpendiculars - property of equliateral triangles

Consider an equilateral triangle ABC P is a point on AB, Q is a point on BC Suppose we draw perpendiculars from P to other sides. Let s1 be the sum of the length of these ...
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### How can I find ratio between area of triangle and area of quadrilateral?

I have a parallelogram $ABCD$. $E$ is center of $AD$. $O$ is center of $AC$ and center of $DB$. $F$ is the intersection point between $CE$ and $DO$. Point $G$ is the intersection between $EO$ and $AF$....
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### Prove that length of three bisectors determine triangle.

All of us know that length of 3 bisectors determine triangle. But actually all proofs that I heard are sufficient large. So I'm interested in short and smart proof. Any ideas?
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### Does three medians determine a triangle?

If given three medians, is there only one triangle that has these three medians? How do I prove that?
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### Points $A,B,C$ are $z_1,z_2$ and $(1-i)z_1+iz_2$ . Then find nature of triangle $ABC$

The points $A,B,C$ represent the complex number $z_1,z_2$ and $(1-i)z_1+iz_2$ respectively on the complex plane. Then triangle $ABC$ is: $(A)$ Isosceles but not right angled $(B)$ Right angled but ...
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### Right triangle on an ellipse, find the area

Beginning note: Please wait until the animations load. The loading might take some time depending on your internet connection. Secondly, the title and the content of the question might not be well ...
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### Area of a triangle on an Argand diagram

I am working on two problems: 1) Find three distinct roots of the equation $8z^3 + 27 = 0$ I solved this and ended up with \begin{align*}z_1 &= \frac32 \left( \cos (\pi/3) + i\sin(\pi/3)\...
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### How to find the area of a triangle with two equations?

So I was given the following problem : ABC is a right angled triangle with the sides $a,b,c$ . Find the area of this triangle, given that $$a+b+c = 22$$ $$a^2+b^2+c^2 = 200$$ I've tried to do a lot ...
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### Defining a region in $\mathbb{R}^2$

I was trying to do this exercise but my answer doesn't match with the solution and I'm wondering why: Consider the coordinates transformation defined by $x=2u+v$ and $y=u^2-v$. Being $T$ the ...
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### Right Triangle Angle problem

I know that this can be easy, but I found it a bit difficult so maybe someone can just explain or give a hint to me. I have a right triangle $ABC$ with points $D$ and $E$ on its hypotenuse so $AB=AE$ ...
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### How to parameterize the interior of a triangle

I would like to know how to parameterize a triangle over $[0,1] \times [0,1]$. I actually only care that the mapping is surjective but a bijection is always nice I suppose. I found this in which an ...