Mathematics Stack Exchange
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Questions tagged [triangles]

For questions about properties and applications of triangles.

A triangle is a polygon with three sides. It is an important geometric figure, because any polygon can be subdivided into triangles.

Triangles can be classified by the number of sides they have that have equal length

  • All three sides of an equilateral triangle have equal length.
  • An isosceles triangle has at least two sides of equal length.
  • A scalene triangle is a triangle that is not isosceles, that is, it has no sides with equal length.

A triangle may also be classified by describing its angles. A triangle is said to be a right triangle if it contains a right angle, and obtuse triangle if it contains an obtuse angle, or an acute triangle if all three of its angles are acute.

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Triangle/Geometry question

How do I solve this triangle question? In the figure below $\Delta OAB$ has an area of $72$ and $\Delta ODC$ has an area of $288$. Find $x$ and $y$.
numbermaniac
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How to find the position of point S on a tetrahedron if all segments are known?

I have been having this problem at work in this software I am writing. This question looks like a homework question but it is not... I promise. I took my problem and generalized it to a more simple form and here it is. Question: So I have this…
spacetimeengineer
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Lemoine Point triangle

from Wolfram MathWorld, I know there is a Lemoine point of triangle, also called symmedian point, the sum of squared distances of this point to all the three sides is algebraically minimum. How can I get the point (X,Y) of the lemoine point when I…
RonYamin
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$A,B,C$ satisfy $\sin 2A: \sin 2B: \sin 2C= 5:12:13$ find $A$?

I would appreciate if somebody could help me with the following problem: Question: $A,B,C$ satisfy (1), (2) (1). $A+B+C=\pi(0< A,B,C< \pi)$ (2). $\sin 2A: \sin 2B: \sin 2C= 5:12:13$ Find $A$ ? I tried by using propertyof triangle function formula…
Young
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Geometry: Finding the sides of the triangle with base and altitude given

The base of an isosceles triangle and the altitude drawn from one of the congruent sides are equal to 18 cm and 15 cm, respectively. Find the lengths of the sides of the triangle. Please help me to solve this. Also, can you please show your…
Ell
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Find side of an equilateral triangle inscribed in a rhombus

The lengths of the diagonals of a rhombus are 6 and 8. An equilateral triangle inscribed in this rhombus has one vertex at an end-point of the shorter diagonal and one side parallel to the longer diagonal. Determine the length of a side of this…
megan
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finding median when all three sides are not given

Let ABC be a triangle with AB=3cm, AC=5cm. If AD is a median drawn from the vertex A to the side BC, then which one of the following is correct? a) AD is always greater than 4cm but less than 5cm b) AD is always greater than 5cm c) AD is always less…
aarbee
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Ratio of Areas of Similar Triangles

First step, I can't find the height. How do you find the height?
user159778
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A triangle problem

In a triangle, the sum of two sides is $x$ and the product of the same two sides is $y$. If $x^2 - c^2=y$ where c is the third side, then what is the ratio of the inradius to the circumradius of the triangle? I guess I have found half of it: if the…
relston mendonsa
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$PC+PD$ is least when the angles $CPA$ and $DPB$ are equal

$C$ and $D$ are two points in the $same$ side if a straight line $AB$ and $P$ is any point in $AB$. Show that $PC+PD$ is least when the angles $CPA$ and $DPB$ are equal No idea how to solve this problem
Apoorv Jain
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Finding the largest angle of a triangle

The sides of a triangle are $(x^2+x+1), (2x+1)$ and $(x^2-1)$. Then what is the largest of the 3 angles of triangle?
Rudstar
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Prove that two triangles are congruent

${ABC}$ and $A'B'C'$ are two triangles. Let $P$ be the midpoint of $BC$ and $P'$ the midpoint of B'C'. Also, $|AP| = |A'P'|$ and $|AC| = |A'C'|$ and $\angle CAB$ = $\angle C'A'B'$. $2|AP| > |AC|$ and $2|A'P'| > |A'C'|$. Prove that triangles $ABC$…
user143883
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Orthocentre of a triangle defined by three lines

Problem: If the orthocentre of the triangle formed by the lines $2x+3y-1=0$,$x+2y-1=0$,$ax+by-1=0$ is at the origin, then $(a,b)$ is given by? I would solve this by finding poins of intersection and the standard text-book methods. But, I was…
Cheeku
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Solving a triangle using the given equation

In a triangle $ABC$ $2a^2+4b^2+c^2=4ab+2ac$ then the numerical value of $cos B$ equals ? ($a,b,c$ are sides opposite to angles $A,B,C$) I tried to use cosine rule , but couldn't adjust terms accordingly, using the given equation. Any hints /…
Simar
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How to prove that:$ BC^2= 3CM^2 + AC^2 $from this triangle problem?

In the triangle $\triangle ABC$, angle $\angle A$ is larger than angle $\angle B$. We choose points $M$ and $N$ at $AB$ such that $AM=MN=NB$. How to prove that: $BC^2= 3CM^2 + AC^2$? Which theorem(s) should I use to prove this problem? Thanks
akusaja
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