# Tagged Questions

For questions about properties and applications of triangles

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### Ratio of bisected cevian in triangle given intersection point

I have the coordinates of points $A$ $B$ and $C$ that form triangle $\triangle ABC$, and the coordinates of a point $D$ inside of $\triangle ABC$. Imagine a cevian, connecting points $A$ and $D$, and ...
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### Find the lengths of sides of a right triangle

If I know the length of the hypotenuse of a right triangle ONLY, is it possible to find the lengths of the remaining 2 sides of that same triangle?
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### Iterating three tangent circles using Malfatti Circles

First, construct three tangent circles (blue circles), then construct the triangle joining their centers. Then construct three Malfatti Circles for this triangle (green circles). Go on. What I'm ...
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### Finding length and width of old square

The area of new shape is $A=130$ m$^2$. The original square had $2$ m added to its width and $5$ m to its length, the problems asks for one of the original sides (since they're all equal of course). ...
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### Is it possible for two triangles to be different if the sides of one is equal to another?

I was reading Euclid's Elements E-book I found online and got stuck on this concept. I will just copy what I found to be very absurd. There could still be another different triangle with the same ...
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### Finding area of sector inside an triangle

I have been asked this question from a junior and could not solve the question in a simple way. I am asking help on this platform. For a triangle $ABC$, Points $D, E$ on $AB$, where $AD:DE:EB=2:2:1$....
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### What will be area of an equilateral triangle? [on hold]

my question is A side of an equilateral triangle is 24 root 3. Inside this triangle two other equilateral triangles is made such that there inner areas becomes same. find out side of smallest ...
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### Solutions of triangles - proof

Question: For a triangle ABC, prove that: $$r_1 + r_2 + r_3 = r + 4R$$ Where $r_1,r_2,r_3$ represent the radius of the ex-circles opposite to angle A, B, and C respectively. $r$ represents the ...
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### Let D be the midpoint of BC in triangle ABC. Let E be the midpoint AD, F be the intersection of line BE with side AC. Find $\frac{AF}{FC}$.

Let D be the midpoint of side BC in triangle ABC. Let E be the midpoint of line AD and let F be the intersection of line BE with side AC. Find $\frac{AF}{FC}$.
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### A problem on triangle and its perpendicular bisectors.

I'm trying to solve the following problem : "In △ABC, coordinates of $B$ are $(−3, 3)$. Equation of the perpendicular bisector of side $AB$ is $2x + y − 7 = 0$. Equation of the perpendicular ...
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### Minimal perimeter of a triangle

Imagine a triangle with a base $[0, s]$ and a height $h$. ($s, h \gt 0$) For what orthocentre $x$ does the triangle have a minimal perimeter and how long is it? Now, the proof starts with: ...
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### Find the length of the side of a right angle triangle inside a circle

Hello Stack Exchange. I have a question which has really been preventing me from making a certain program.In my program I need to find the length of AC using only AB and BD.The triangle is right-...
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### A box contains 5 rods whose lengths make triangles.

A box contains five rods whose lengths are 1", 3", 6", 10", 15". How many different obtuse triangles can be made using only three rods at a time. I determined that the answer is 1 because the ...
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### How to find heading angle to an object whose x,y coordinates are known?

Scenario: I have a map with a marked location on it. I know my x,y coordinates on the map (top left corner is 0,0), my distance from that marked location, my heading angle relative to true north (0 is ...
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### Problem on Equilateral Triangle and points

Equilateral $\triangle{ABC}$ with sides $2\sqrt{3}$. Let $P$ be the point outside$\triangle{ABC}$ such that points $A$ and $P$ lie opposite to $BC$. Let $PD$, $PE$, $PF$ be the perpendicular dropped ...
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### Tracing the sides of an equilateral triangle

Is there any way I can get the points in 2D plane on the sides of an equilateral triangle for certain infinite animation sequence? For example in case of tracing the circumference of the circle, I ...
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### Sides of triangle are in A.P., find its perimeter

The sides of a triangle are in Arithmetic Progression $(A.P.).$ If the smallest angle of the triangle is $\alpha$ and largest angle of the triangle exceeds smallest angle by $\beta$ , then what is the ...
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### How do I find the partial derivatives of heron's formula?

Heron's formula finds the area $A$ of a triangle with sides of length $a$, $b$, and $c$: $$A=\sqrt{s(s-a)(s-b)(s-c)}$$ where $s$ is the semiperimeter of the triangle: $$s=\frac{a+b+c}{2}$$ How do ...
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### Geometric arithmetic: triangular number triples [closed]

Call a triple $x, y,$ and $z$ of numbers triangular if and only if there is a triangle whose sides are in the triple ratio $x:y:z$. Since the sum of two sides of a triangle exceeds the remaining side, ...
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### How to find the type of triangle when given the ratio of it's sides?

Q.The sides of a triangle are in ratio 4 : 6 : 7, then the triangle is: (A) acute angled (B) obtuse angled (C) right angled (D) impossible It's definitely not (C) right-angled ...
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### Solve linear system with $A_{i,j} = \langle e_i, e_j\rangle^2$, edges of a triangle

I have three vectors in $e_i\in\mathbb{R}^3$ that form a triangle. Let us consider now the linear equation system $Ax=b$ with $$A_{i,j} = \langle e_i, e_j\rangle^2,\\ b_i = \langle e_i, e_i\rangle.$$...
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### Identifying a triangle in the 3d-space as acute, obtuse, right or equilateral

Triangle $ABC$ has vertices $A(-1, 1, 3)$, $B(-1, 3, 5)$, and $C(-3, 3, 3)$. What kind of triangle is $ABC$? Justify your answer. So far all I have done is I found the distance between $AB$, $BC$ ...
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### On constructing a triangle given the circumradius, inradius, and altitude .

I was recently pondering about constructing triangles given different attributes of it. I am wondering whether we could construct a triangle given its Circumradius $R$ , Inradius $r$, and length ...
In $\Delta ABC$, the bisector of $\angle A$ intersects $BC$ at $D$. The perpendicular to $AD$ from $B$ intersects $AD$ at $E$. The line through $E$ parallel to $AC$ intersects $BC$ at $G$, and $AB$ at ...