For questions about properties and applications of triangles

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1answer
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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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3answers
101 views

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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2answers
30 views

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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0answers
23 views

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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0answers
37 views

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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1answer
53 views

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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1answer
31 views

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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1answer
84 views

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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1answer
44 views

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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1answer
22 views

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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3answers
106 views

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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1answer
72 views

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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2answers
39 views

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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1answer
19 views

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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1answer
21 views

Coordinates along lines in a Triangle

I've just lumbered myself with a bit of a maths problem. I have the triangle below Its 3 points are at these coordinates - $(-4.2,0),\,(0, 2.7),\,(5, 0)$. I know all of my coordinates along the $...
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0answers
17 views

Calculate the percentage of a triangle inside a cuboid?

I have a large (order 10^7) collection of triangles in 3D space. I also have a cuboidal mesh also of order 10^7. For each triangle I need to calculate the area of that triangle which is inside any of ...
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1answer
28 views

Maximum area of a triangle when perimeter is fixed.

I can't solve the following problem: Show that amongst all triangles with perimeter $3p,$ the equilateral triangle with side $p$ has the largest area. Further show that $9p^2\ge 12\sqrt{3}\Delta.$ ...
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4answers
48 views

Is this a correct way to solve this high school coordinate geometry question?

Here's the question: Given point $A$: $(-3;-1)$ Given point $B$: $(3;7)$ Given point $Z$: $(x;0)$ Find the $x$ coordinate of point $Z$ so that the angle of view of AB segment is $90$ ...
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1answer
59 views

Sine law and circumscribed circle

How is $\frac{a}{\sin(A)}=2R$ (where $R$ is the radius) derived?
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2answers
41 views

Find angle of a right triangle.

Ok, so this question is from a practice exam. Looks very simple and basic, but I'm not very good at math, so I'm having trouble setting up the problem. One acute angle of a right triangle is not ...
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0answers
25 views

Angles and How they Correspond to Sides of a Triangle

I have done some Googling but am not sure what question I need to ask. I came here instead. I am at a 9th grade math level (Geometry) and working on a problem that is asking me to find x and y based ...
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1answer
52 views

Generic formula for third point of triangle knowing the other two points and all the side lengths

My question is similar to this one, but the solution provided makes use of some 'properties' that will not be true for all triangles. For example, if point A is not in the origin, or point B is not in ...
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2answers
63 views

How does the way we define cos or tan have anything to do with degrees of the angle?

So sine of angle $A$ is just a ratio. It is the ratio of the length of the opposite or perpendicular of angle $A$ and the hypotenuse. Cosine of angle $A$ is also just a ratio. It is the ratio of the ...
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0answers
29 views

Why we name one side as the perpendicular of an angle but does not actually define it?

If I have a right angled triange: $\qquad \qquad \qquad \qquad$ I was wondering why we name the sides like this? The base of $A$ kind of make sense. But the perpendicular of $A$ what relation does it ...
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0answers
20 views

Construction of a triangle using symmetry

I need to construct a triangle $\Delta \textrm{ABC}$ knowing that $t_a = AS$, $|AS| = 6\, cm$, $|\measuredangle \textrm{BCA}| = 30°$ and $|AB| = 5.5 \,cm$. I've been told that it's possible to do it ...
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1answer
24 views

Find altitude of equilateral triangle given inscribed circle dimensions and position

I've found myself trying to solve this for my Geometry class where we have to model a basic piece of architecture and find its volume and surface area (very basic). But the structure I chose requires ...
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1answer
32 views

Given a triangle $ABC$, Find a point $P$ such that $PA:PB:PC=1:2:3.$ [closed]

"Given a triangle $ABC$, Find a point $P$ such that $PA:PB:PC=1:2:3.$ I found this on a Olympiad book, and I was unable to solve it. Any help will be appreciated.
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1answer
51 views

Question about area and triangle

Problem: Consider the following diagram. in $\triangle$ABC: Areas: $\triangle$AOM = a $\triangle$POC = b $\triangle$NOC = c $\triangle$BON = d. Find the area of $\triangle$MOB and $\...
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1answer
27 views

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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1answer
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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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1answer
82 views

In a triangle $ABC$ with side $AB=AC$ and $\angle BAC=20 ^\circ $. $D $ is a point on side $AC$ and $BC = AD$. Find $ \angle DBC$

Problem : In a triangle $ABC$ with side $AB=AC$ and $\angle BAC=20 ^\circ $. $D $ is a point on side $AC$ and $BC = AD$. Find $ \angle DBC$ Solution: $AB =AC$ So $ \angle ACB = \angle ABC$ $ \...
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1answer
31 views

Solve using Law of Cosines or Law of Sines

I'm trying to solve these sets of problems please. Determine the number of triangles with the given parts and solve each triangle (if possible). $\alpha=39.6^\circ,c=18.4,a=3.7$ $\gamma=60^\circ,b=...
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1answer
43 views

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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2answers
51 views

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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1answer
42 views

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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1answer
20 views

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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1answer
273 views

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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0answers
35 views

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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6answers
40 views

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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1answer
22 views

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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1answer
21 views

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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2answers
48 views

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 ...
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Triangle angle question [closed]

I need help about a triangle angle question.
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1answer
25 views

For any point inside a triangle

Let $P$ be an interior point of the triangle $\triangle ABC$. Assume that $AP$, $BP$ and $CP$ meet the opposite sides $BC$, $CA$ and $AB$ at $D$, $E$ and $F$, respectively. Show that $\frac{AF}{FB} +\...
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0answers
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Similar Triangle dissections

Andrzej Zak found that a triangle with sides based on powers of the root $d^6-d^2-1=0$, $(d=1.15096...)$ that can replicate itself with 6 differently sized copies. The numbers are powers of $d$. The ...
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0answers
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An interesting geometry problem with angle bisectors and tangent

I have found the following problem: There is an acute $\triangle ABC$. Denote its circumcircle as $\omega$. The angle bisector of $\angle BAC$ intersects $BC$ and $\omega$ in points respectively $A_1$ ...
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1answer
57 views

Distance between incentre and orthocentre.

I want to prove that the distance between incentre and orthocentre is $$\sqrt{2r^2-4R^2\cos A\cos B\cos C} $$here $r$ is inradius and $R$ is circumradius. I considered $\triangle API$ ($P$ is ...
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2answers
274 views

How do squares of non-right triangles relate?

How do squares of the sides of a triangle, any triangle, relate?
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2answers
56 views

2 circles in an isosceles triangle

I've been given the following school problem: ABC is an isosceles triangle (AB = AC). The radius of the incircle is R and of the other circle (which is tangent to the incircle and to the legs of ...
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2answers
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Triangle group $(\beta,\beta,\gamma)$ is a subgroup of the triangle group $(2,\beta, 2\gamma)$.

Let $1/\alpha+1/\beta+1/\gamma<1$, and let us consider the triangle group $(\alpha,\beta,\gamma)$, i.e. the subgroup of $\mathbb{P}\mathrm{SL}(2,\mathbb{R})$ induced by the hyperbolic triangle ...