For questions about properties and applications of triangles

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5
votes
4answers
141 views

Is there an integer that $\sqrt{3}$ can be multiplied by that will produce a whole integer?

The question came up while messing around with graph paper. I wanted to make an isosceles triangle where the length of one side and it's hight were both integers. The closest I could get was a base ...
4
votes
2answers
230 views

Does “triangle” in English exclude degenerate triangles?

Just for fun read few problems on the projeteuler.net website. Number 276 found interesting: Consider the triangles with integer sides a, b and c with a ≤ b ≤ c. An integer sided triangle ...
4
votes
1answer
1k views

Finding the distance between two gears

I have the following problem: In my class, we did a majorly complicated method to figure this out but I think there is a better way to do this... Here is the exact problem: A belt fits snugly ...
3
votes
3answers
56 views

Right-Angled Isosceles Triangle covering puzzle

Consider a RAIT (right-angled isosceles triangle), from which we remove a RAIT smaller than half its area by a cut perpendicular to the hypotenuse, like this: How many RAITs are required to cover ...
3
votes
2answers
185 views

How do you find the height of a triangle given $3$ angles and the base side? Image given.

This question has me absolutely stumped. This is the image of the question, how can I work out $x$? I've been doing a variety of attempts but I just cant get it.
3
votes
3answers
492 views

How many triangles can be created from a grid of certain dimensions?

How would you determine how many non-degenerate triangles can be drawn by connecting points in a $5 \times 5$ grid?
2
votes
2answers
76 views

Equal perimeters of squares and right angled isosceles triangles

Consider a square ABCD having length l and breadth. Now start folding the sides AB and AC so that the figure becomes something like this $$$$ All the vertical and horizontal folds/stairs are equal in ...
2
votes
1answer
64 views

Distances to line passing through the centroid of triangle

Let $p$ be a line that pass through the centroid of a triangle $ABC$. Unless the line pass through one vertex, then $2$ verices are one side of the line, while the third one is on the other side. ...
2
votes
1answer
330 views

Calculate angle of triangle

I need to calculate the angle between two sides, I have the length of A & B sides, but don't know how to find the angle... Both sides are the same length. I can get the start and end vectors of ...
2
votes
1answer
69 views

find parameter for maximize area

suppose that we have Cartesian coordinate system.and suppose that we have three point which depend on parameter $t$,where t belongs to $(0,1)$;points are $A(cos(3-t),sin(3-t))$ $B(cos(t),sin(t))$ ...
2
votes
1answer
366 views

Move Point A along a line

Sorry, can't post images if my rep is below 10, and can't post more than 2 links. I removed the http section so it won't count as a link. I hope this isn't against forum rules, I'm not hurting anyone. ...
2
votes
3answers
350 views

Geometry - Equilateral triangle covered with five circles

I have to cover an equilateral triangle (whose sides are 1m long) with 5 identical circles: what's the minimum radius of the circles?
2
votes
2answers
7k views

Finding the area of triangle if length of medians are given

My question is: In triangle ABC ,length of median from vertex A is $13$ , length of median from vertex B is $14$ , length of median from vertex C is $15$. Compute the area of triangle ABC.
1
vote
3answers
162 views

Prove that point M is on circle c

It's hard to create question names that make sense. Anyhow, the following is another question from my math assignment. Line-segment AB has a fixed length of 10 units. point A moves on the positive ...
1
vote
4answers
182 views

Inverse triangle equality [duplicate]

Possible Duplicate: Why exactly can you take the absolute value of one side of this inequality and assume it is still true? Why is $||a|-|b|| \ge |a|-|b|$, tried a lot (like comparing to ...
0
votes
2answers
47 views

No. of equilateral triangles required to completely fill a bigger equilateral triangle

$\triangle ABC$ is equilateral with side length=2.1cm Smaller equilateral triangles with side length=1cm are placed over $\triangle ABC$ so that it is fully covered. Find the minimum number of such ...
0
votes
1answer
87 views

Prove vertex-orthocenter distance is twice of side_midpoint-circumcenter distance

$AL$ , $BM$ , $CN$ are altitudes , $TD$ , $RF$ , $ES$ are perpendicular bisectors of sides. How to prove $AQ = 2PD$ ? By similar triangles $\triangle AQN \sim \triangle CQL$ and $ \triangle CQL \sim ...
0
votes
1answer
751 views

Proof of ASA , SAS , RHS , SSS congruency theorem

I have tried searching in many places for some good proofs of these theorems but couldn't find them anywhere . Even my math teacher cannot explain it to me and says that these theorems just work. I ...
0
votes
1answer
1k views

Solving triangles and quadratic equations

When calculating the pieces in a triangle with only two sides and an intermediate angle is known, one must solve a quadratic equation. By solving the equation are 2, 1 or 0 solutions, as ...
-2
votes
1answer
1k views

How to prove we could use mass point geometry to solve all the triangle problem involving ratio between line segment and transversal in a triangle?

what is an easy way to prove that use mass point geometry to solve a problem in the link i provide that is involving cevians in a triangle is same as using the other way in euclidean geometry or ...