For questions about properties and applications of triangles

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8
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3answers
91 views

Dividing an obtuse triangle into acute triangles

Can an obtuse triangle be subdivided into only acute triangles (right triangles are not allowed)? Any number of subdivisions can be made as long as all of the angles in all resulting triangles are ...
0
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1answer
22 views

In this figure find AC=x

Can you find $AC$, when only the angle $DBC$ and $DEB$ are $90$ grades. I can't because I think they should give the angle $CAB=90$ grades too.
1
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1answer
39 views

Euclid I.24 Proof Why is DFG greater than EGF?

Proposition 24 If two triangles have two sides equal to two sides respectively, but have one of the angles contained by the equal straight lines greater than the other, then they also have the ...
2
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1answer
49 views

To prove in a triangle: $AD^2=AB\cdot AC- BD\cdot CD$

If $AD$ is an angle bisector of $\triangle ABC$ (with $D\in BC$), then we have to prove that: $$AD^2=AB\cdot AC- BD\cdot CD$$ I have no idea how to do this, can this be proved with simple geometry? ...
0
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1answer
25 views

Lengths of the sides of a triangle: sufficient and necessary condition?

For any three positive scales, $a,b,c$, what is the sufficient and necessary condition such that they can form a triangle? Is $a+c>b,a+b>c,b+c>a$ enough? Thanks!
1
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0answers
28 views

Circles intersecting at A and B [duplicate]

Question: Two given circles intersect at A and B. A straight line through B meets the circles again at C and D. Prove that CD is greatest when it is parallel to the line joining the centres My ...
4
votes
3answers
183 views

Trigonometry. Finding the angle alpha

Refer the diagram below : What should be the angle alpha such that the variable x is between 7mm and 7.3mm.
0
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2answers
37 views

Isosceles triangle and scalene triangle

Question: Given the base and vertical angle of a triangle show that its area is greatest when the triangle is isosceles. My attempt: For isosceles triangle (with base given 2x, and vertical ...
0
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1answer
59 views

Can we find out the area of conical frustum by using triangles?

I have been trying to find out the area of conical frustum by using triangles.
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4answers
975 views

Does a triangle always have a point where each side subtends equal 120° angles?

Is there a point $O$ inside a triangle $\triangle ABC$ (any triangle) such that the angle $\angle{AOB} = \angle{BOC} = \angle{AOC}$? What do we call this point?
1
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0answers
22 views

Triangles with vertices on conics and their foci

Let $A$, $B$, and $C$ be the lengths of the three sides of a triangle. Let $α$, $β$, and $γ$ be the measures of the angles opposite those three sides respectively. Mollweide's formula tells us that ...
0
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1answer
53 views

applied optimization problem- triangle fence

A farmer is trying to fence off a field on the edge of a river. He has two 1km long sections of fence to use to make a triangular field. The edge by the river does not need fencing, and the fence ...
0
votes
2answers
58 views

The height of a right triangle with legs $a,b$ is equal to $ab/\sqrt{a^2+b^2}$ [closed]

The height of a right triangle with legs $a,b$ is equal to $ab/\sqrt{a^2+b^2}$ Need help with number ii since it asks for a uncommon way of approaching the problem.
0
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1answer
25 views

Question - Corresponding parts of congruent triangles

Please answer the question below with these specifications: If the answer is yes write a paragraph proof to show which congruence shortcut utilized. Show all rules of geometry that are applied to ...
4
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1answer
36 views

Is a triangle with two equal angles always isosceles?

An isosceles triangle is a triangle with two sides that are equal in length. This means that two angle will also be equal to each other. Is there any way that a triangle could have two (only two) ...
0
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1answer
29 views

Related rates question.

Two sides of a triangle have lengths $\sqrt{21}~m$ and $\sqrt{7}~m$. The angle between them is increasing at a rate of $\dfrac{2}{\sqrt{3}}~rad/sec$. How fast is the altitude of the triangle ...
2
votes
3answers
53 views

Geometry question involving triangle

Question: $ABC$ is a right angle triangle at $A$. $AD$ is the altitude through A; E is a point on AC such that $AE=CD$. F is a poibnt on AB such that $AF=BD$. Prove that $BE=CF$. Challenge ...
0
votes
3answers
49 views

Getting 90 degree coordinate of 2 coordinates that you know

I have 2 coordinates and I need to find the third with a 90 degree angle. How could I do this? ...
1
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4answers
87 views

Geometry question involving triangles given with picture.

Here's the question: $\overset{\Delta}{ABC}$ is a triangle. $D$ is a point on $[BC]$. $|BD|=4$. $|AD|=|CD|$. $\text m(\widehat{CBA})=\alpha=30^\circ$. $\text ...
1
vote
1answer
32 views

How Many Triangles are Created by n Lines in the Plane?

Suppose we are given n lines in the plane in "general position", which in the present case we define to mean the following: A. no 2 lines are parallel or identical B. no 3 lines have common ...
1
vote
1answer
44 views

Area of Triangle

The position vectors of $A$ $B$ and $C$ relative to an origin $O$ are given by $OA=(2,1,3)$ $OB=(0,-1,7)$ and $OC=(2,4,7)$ Part i) Show that angle $BAC= \cos^{-1}(\frac{1}{3})$ Part ii) Using the ...
1
vote
0answers
44 views

Find all the triangles satisfying $\cos(A)\cos(B)+\sin(A)\sin(B)\sin(C)=1$ [duplicate]

I am trying to solve the problem of finding all triangles with angles $A$, $B$ and $C$ (in $[0,\pi]$) such that $\cos A\cos B+\sin A\sin B\sin C=1$. In the case where the triangle has a right angle, ...
0
votes
4answers
100 views

How can I find the lenght of the third side of any triangle

I will know the length of two sides of any triangle that I use, but I will not know any of the angles. I know how to find the length of the third side if I knew the angle where I am sitting, but how ...
0
votes
1answer
23 views

Find the edges of a triangle from a vertex

If I have a series of three vertices that make up a triangle, how can I take one of these vertices and find the edges that go from that vertex to the other two vertices?
0
votes
1answer
54 views

The Sine Law: A Simplified Criterion for the Ambiguous Case?

Here is my suggestion for an issue that doesn't seem to be handled well in any online notes that I have seen. Can anyone give a counter-example? If you are given $a,b,$ and $B$ in $\triangle ABC$ ...
0
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1answer
26 views

Triangle problem about a point

Question: If D is a point on the side AB of ABC, find a point X on BC such that the triangles XAD and CAX are equal in area. My attempt: I don't actually know how do I solve this problem. I ...
1
vote
1answer
42 views

Geometry and triangles problem

Question: If D be the mid-point of AB and if the internal bisectors of $\angle ADC$ and $\angle BDC$ meet $AC$ and $BC$ at H and I respectively. Prove that $HI \parallel AB$ My attempt: It is ...
2
votes
1answer
37 views

How to find the number of right angled triangles with integer sides and inradius 2009 ..

Problem : How to find the number of right angled triangles with integer sides and inradius 2009 Please help on this as I am not getting any clue how to proceed this problem. I know that ...
2
votes
2answers
34 views

Trigonometry : Find the length of side

Can someone tell me how to calculate the length 'd' from the below figure? It is from Lecture 06 - Optical flow : ...
1
vote
1answer
43 views

A right triangle's incenter problem by pure geometry..

$ABC$ is a right triangle such that $\angle B= 90^{\circ}$ and $BD$ is the altitude to $AC$. Given that: $I$ is the incenter of $\triangle ABC$, $I_1$ is the incenter of $\triangle ABD$ and $I_2$ ...
0
votes
2answers
53 views

Intersection of a median of a triangle with another line segment

In triangle ABC, M is the midpoint of |BC| and D is the interior point of |AB|. Point E is the intersection of the sides |AM| and |CD|. Prove that if |AD| = |DE|, then |AB| = |CE|. I know that this ...
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vote
1answer
28 views

How can I find Triangle base length?

How can I find base length of the triangle in attached picture? Can I use mid-segment theorem to find the base? Thanks in advance
1
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2answers
61 views

Properties of triangles in non-Euclidean geometries

As we all know, the angles in all triangles in Euclidean geometry must add up to $180^\circ$. As some of us may know, this is not true in non-Euclidean geometries; for example, on the surface of a ...
0
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1answer
18 views

Choosing the angle in rectangular coordinates

Find all possible polar coordinates for the point P that has rectangular coordinates ( -2,2 (3)^(1/2) ). At the end, the equation satisfied by which angle ? How to know it ? The cos angle or the sin ...
0
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1answer
29 views

Find the plane a triangle lies on

I am trying to determine if the plane on which two triangles lie intersects for a collision-detection implementation. Unfortunately, I'm stuck at step one, which is finding the plane on which a ...
0
votes
3answers
25 views

How can I calculate angles between objects at the sky?

There is a polar coordinate system which represents the sky from an observer. The elevation angle is 0 to 90 degrees which corresponds to horizon to zenith. The azimuth angle is 0 degrees (north) ...
0
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0answers
20 views

Filling an Obtuse Triangle with Equilateral Triangles or a Pre-Defined Shape

I am creating an obtuse triangle of undetermined proportions and I need to find how to fill it with equilateral triangles or a pre-defined shape that can fill it. Any math I've done has been, and is ...
2
votes
2answers
67 views

Finding the length of the side of the equilateral triangle

Here, ABCD is a rectangle, and BC = 3 cm. An Equilateral triangle XYZ is inscribed inside the rectangle as shown in the figure where YE = 2 cm. YE is perpendicular to DC. Calculate the length of the ...
0
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1answer
50 views

Calculate point P(x,y) in a circle given a radius and angle degree

I'm doing a program in Java to draw a PieChart based on given value as link below. data for piechart Given that the diameter, radius, angle degree, center point (150,150) and First Point A (150,0) ...
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1answer
22 views

Dealing with negative areas— coordinate geometry

Question: Find the area of a quadrilateral in the Cartesian plane, whose vertices are (-4, 5), (0, 7), (5, -5) and (-4, -2) My solution: [I meant to draw ...
1
vote
2answers
46 views

Given the area and perimeter of a triangle, find its coordinates

How can we find the coordinates of a triangle, given its area and perimeter? (We can find any triangle that satisfies the given area and perimeter) I tried to find the lengths of the sides of the ...
0
votes
1answer
26 views

Find the sum of the lengths of line segments $BD$ and $CE$

sorry for the drawing. From a point $D$ on side $AB$, a line $DE$ is drawn through a point $E$ on side $AC$ such that angle $AED$ is equal to angle $ABC$. If the perimeter of the triangle $ADE$ is ...
1
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1answer
33 views

If $|\alpha|\leq 1$ and $|\beta|\leq 1$, prove that $|\alpha+\beta|\leq |1+\overline{\alpha}\beta|$

Note $\alpha$ and $\beta$ are complex numbers and $\overline{\alpha}$ is the conjugate of $\alpha$. I've tried using variations of the triangle inequality and I couldn't find anything to work.
1
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1answer
225 views

Proof of a certain lemma in geometry

In the following article: http://yufeizhao.com/olympiad/geolemmas.pdf in the proof of the fact about the diameter of the incircle on page 2, the author claims that the proof that $BD = CF$ follows ...
0
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0answers
36 views

How many are there triangles with different rational sides, rational area, bisectrixes and 1 rational median?

I've been searching triangles with all elements being rational numbers. However, I've found somewhere on Internet proof that it's not possible. Then, I was searching triangles with maximal possible ...
7
votes
1answer
136 views

Can the $9$ point circle be generalized to $n$-gons of $n\gt3$?

All triangles have concyclic vertices and have a $9$ point circle which intersects the triangle's feet and the midpoints of its sides (as well as $3$ other significant points). Is this special for ...
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2answers
41 views

Find the Angle BAC

AB,AC,BC and h are known and its a isosceles triangle how to find angle BAC?
0
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2answers
22 views

Value of the angle in isosceles triangle.

I try to find a way to calculate value of one of the isosceles triangle angles when I have given values of its height h = 200 and base ...
3
votes
1answer
38 views

Triangles, flagpoles and heights, oh my!

Here is a math question i got from school: On a horizontal plane, there are two flagpoles. One is 20m, and the other is 10m. There is a wire connected from the top of each flagpole, to the bottom of ...
0
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1answer
33 views

Is any property of orthocenter related in this question?

While practicing mathematics Olympiad questions , i got the below given question . Though the solution is given , I am not able to bypass certain steps ... Can anyone please explain me why angle KPA ...