For questions about properties and applications of triangles

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2answers
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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.
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1answer
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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 ...
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1answer
34 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) ...
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1answer
28 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 ...
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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 ...
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3answers
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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? ...
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4answers
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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 ...
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1answer
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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 ...
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1answer
38 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 ...
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0answers
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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, ...
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4answers
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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 ...
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1answer
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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?
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1answer
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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 $\triangle ABC$ ...
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1answer
24 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 ...
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1answer
40 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 ...
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1answer
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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 ...
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2answers
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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 : ...
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1answer
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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 $I_2$ ...
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2answers
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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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1answer
27 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
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0answers
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Circumcentre of three points X, Y, Z, given distance from each to points A and B

I'm racking my brain trying to figure out where to start on this, and it's been too many years since working on these kinds of problems. I have six measurements which I'd like to use to calculate a ...
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1answer
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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 ...
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1answer
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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 ...
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1answer
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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 ...
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3answers
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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) ...
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0answers
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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 ...
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2answers
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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 ...
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1answer
24 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
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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 ...
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2answers
39 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 ...
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1answer
22 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 ...
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1answer
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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.
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1answer
224 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 ...
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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 ...
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1answer
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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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Special Right-angled Triangles

How do I solve number 11-12? I'm in 2nd year junior high from Indonesia. I don't understand this at all, since I was absent during the first class about this. I do know that there are 2 special right ...
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2answers
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Find the Angle BAC

AB,AC,BC and h are known and its a isosceles triangle how to find angle BAC?
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2answers
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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 ...
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1answer
35 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 ...
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1answer
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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 ...
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2answers
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CD is height of right-angled triangle ABC, M and N are midpoints of CD and BD: prove AM⊥CN

I was having some troubles proving this: CD is the height that corresponds to the hypotenuse of right-angled triangle ABC. If M and N are midpoints of CD and BD, prove that AM is perpendicular to CN. ...
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1answer
40 views

Distance over Time and the Pythagorean Theroem

I know the Pythagorean thereom for the last part. I am not $100\%$ sure with the other parts. Here is the problem: Marty and Rediat got in a fight. They walked away from each other on seperate paths ...
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Issue with a right-angled triangle

The area of the right angle triangle is $18\text{ cm}^2$ and the ratio of its legs is $2:3$. What is the length of the hypotenuse? I assumed the lengths of two sides to be $2x$ and $3x$. I used ...
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1answer
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Which of the following are the correct angle measures for angles 1 and 2 in the triangle shown below?

http://www.explorelearning.com/ELContent/gizmos/ELMath_Deliverable/ExplorationGuides/Geometry/images/EL_GEO_TriSum6.gif A. mangle1 = 43°, mangle2 = 137° B. mangle1 = 137°, mangle2 = 43° C. mangle1 ...
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1answer
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Given a particular triangle that has been constructed, I want to prove that one of the angles must be $> 45$ degrees. [duplicate]

Suppose you are given an acute triangle $XYZ$ with the following properties: At $\angle XZY$, the $\angle$ bisector is drawn and extended all the way to $XY$. Lets call the point where it intersects ...
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2answers
51 views

Two triangles with two equal sides and equal area will have the third size also equal?

Consider two triangles $\triangle abc$ and $\triangle def$ such that $ab=de$ and $ac=df$.Also area of $\triangle abc$ is equal to area of $\triangle def$.Now draw $cm$ perpendicular to $ab$ and $fn$ ...
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0answers
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Two questions about triangle that blocked at rectangle…

The area of the triangle is equal to the half area of the rectangle? The center point of the triangle is same as the center point of the rectangle? About 2 - if not, how do I calculate the center? ...
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2answers
33 views

Calculating the perimeter of triangle inside of a circle

In triangle $DCB$, $BC = 10$ and is also the diameter. If the area of triangle $DCB = 11$, then determine the perimeter of the triangle. I am a little stuck on this problem. I tried using the sine ...
4
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2answers
807 views

Triangle in Triangle

I have the lengths of three sides of an acute triangle ABC as shown below. Assume a point P on the side AB such that, if Q is the projection of P onto BC, R is the projection of Q onto CA, P becomes ...
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1answer
27 views

Will two triangles with two equal sides and equal area have same altitude

Consider two triangles ABC and DEF.AB=DE and AC=DF .Also area of triangle ABC is equal to the area of triangle DEF.If we draw an altitude (to one of the equal sides) in both triangles, is it(altitude) ...